Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7 - Common Core: High School - Statistics and Probability

Card 0 of 15

Question

A professor conducts a study on the relationship between sleep and academic performance by asking his 420 students how many hours of sleep they missed while studying for the class final.

The regression output is as follows:

Which of the following statements is TRUE?

Answer

No explanation available

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Y x 1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line. Lets observe the point where the line crosses the x-axis and the point to where it crosses , positive five, on the x-axis.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We find that the slope of the equation is one. We can also calculate the slope by using the traditional "rise over run" definition. If we count blocks on the graph we can see that for every six blocks that it "rises," it "runs" six blocks. In other words, the slope increases one block in the x-direction as it increases one block in the y-direction; therefore, the slope is one (see figure below).

Y x 1 slope

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Y x 1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line. Lets observe the point where the line crosses the x-axis and the point to where it crosses , positive five, on the x-axis.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is one. We can also calculate the slope by using the traditional "rise over run" definition. If we count blocks on the graph, then we can see that for every six blocks that it "rises," it "runs" six blocks. In other words, the slope increases one block in the x-direction as it increases one block in the y-direction; therefore, the slope is one (see figure below).

Y x 1 slope

Compare your answer with the correct one above

Question

Identify the y-intercept of the following line:

Y x 1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The y-intercept represents the point where the line intersects the y-axis. We can identify the y-intercept by locating it on the graph (see the red circle in the figure below).

Y x 1 intercept

The y-intercept is located at the following point:

They correct y-intercept is as follows:

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot2.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 11 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 44 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 11 block in the y-direction; therefore, the slope is 11 (see figure below)

Plot2.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot3.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 5 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 20 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 5 block in the y-direction; therefore, the slope is 5 (see figure below)

Plot3.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot4.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

m=\textup{slope}

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

m=\frac{\Delta y}{\Delta x}

m=\frac{y_2-y_1}{x_2-x_1}

In this formula, the x- and y-values come from two points from the line written in the following format:

(x,y)

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

\left( -2 , -15 \right) and \left( 2 , 53 \right)

Now, substitute these numbers into the slope formula.

\\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{ 53 - -15 }{ 2 - -2 } \\ \\ m=\frac{ 68 }{ 4 } \\ \\ m= 17.0

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 17 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 68 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 17 block in the y-direction; therefore, the slope is 17 (see figure below)

Plot4.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot5.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 10 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 40 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 10 block in the y-direction; therefore, the slope is 10 (see figure below)

Plot5.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot6.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 15 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 60 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 15 block in the y-direction; therefore, the slope is 15 (see figure below)

Plot6.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot7.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 16 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 64 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 16 block in the y-direction; therefore, the slope is 16 (see figure below)

Plot7.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot8.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 15 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 60 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 15 block in the y-direction; therefore, the slope is 15 (see figure below)

Plot8.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot9.1

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 6 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 24 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 6 block in the y-direction; therefore, the slope is 6 (see figure below)

Plot9.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 13 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 52 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 13 block in the y-direction; therefore, the slope is 13 (see figure below)

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 3 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 12 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 3 block in the y-direction; therefore, the slope is 3 (see figure below)

Plot11.2

Compare your answer with the correct one above

Question

Identify the slope of the following line:

Plot11.2

Answer

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 7 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 28 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 7 block in the y-direction; therefore, the slope is 7 (see figure below)

Plot12.2

Compare your answer with the correct one above

Tap the card to reveal the answer