Slope and Line Equations - Algebra 1

Card 0 of 20

Question

What is the slope of the equation 4_x_ + 3_y_ = 7?

Answer

We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4_x_ + 3_y_ = 7.

Isolate the y term: 3_y_ = 7 – 4_x_

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

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Question

Find the slope of the line through the points (6,2) and (3,4).

Answer

The equation for slope is $\frac{(y_2-y_1)}{(x_2-x_1)}$ . You plug in the coordinates from the points given you, and get $\frac{(4-2)}{(3-6)}$ , giving you $\frac{2}{-3}$ . Note that it does not matter which point you use as point 1 and point 2, as long as you are consistent.

$\frac{(y_2-y_1)}{(x_2-x_1)}$

(6,2) = (x1,y1)

(3,4) = (x2,y2)

$\frac{(4-2)}{(3-6)}=\frac{2}{-3}=-\frac{2}{3}$

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Question

Given the line 4y = 2x + 1, what is the slope of this line?

Answer

4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.

4y = 2x + 1

(4y)/4 = (2x)/4 + (1)/4

y = 0.5x + 0.25

y = mx + b, where the slope is equal to m.

The coefficient is 0.5, so the slope is 1/2.

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Question

If (1,2) and (4,6) are on the same line, what is the slope of the line?

Answer

$m=slope=\frac{\Delta y}{\Delta x}=\frac{\left ( y_{2}-y_{1}\right )}{\left ( x_{2}-x_{1}\right )}=$

$\frac{\left ( 6-2\right )}{\left ( 4-1\right )}=\frac{4}{3}$

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Question

The equation of a line is:

What is the slope of the line?

Answer

Solve the equation for

where is the slope of the line:

$y=-\left ( \frac{5}{25} \right )x+\frac{14}{25}=-\left ( \frac{1}{5} \right )x+\frac{14}{25}$

$Slope=-\frac{1}{5}$

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Question

What is the slope of the line containing the points (7,12) and (91,32).

Answer

To find the slope of a line you must first assign variables to each point. It does not matter which points get which variables as long as you keep the $x_{1}$ and $y_{1}$ and $x_{2}$ and $y_{2}$ consistent when you plug them into the equation.

Then we plug in the variables to this equation where represents the slope. $m=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}$

Then we plug in our points for $x_{1},x_{2},y_{1},and\ y_{2}$ and the example looks like $m=\frac{(32-12)}{(91-7)}$

Then we perform the necessary subtraction and division to find an answer of $m=\frac{20}{84}=\frac{5}{21}$

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Question

A line passes through the points and . What is its slope?

Answer

The slope is the rise over the run. The line drops in -coordinates by 13 while gaining 5 in the -coordinates.

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Question

$\textup{What is the slope of the linear equation }3y-4x=13\textup{ ?}$

Answer

$\textup{To find the slope, put the equation into }y=mx+b\textup{ format.}$

$y = \frac{4}{3}x+\frac{13}{3};;;;;;\textup{slope}=m = \frac{4}{3}$

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Question

Which of the following is an example of an equation written in slope-intercept form?

Answer

Slope intercept form is , where is the slope and is the y-intercept.

is the correct answer. The line has a slope of and a y-intercept equal to .

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Question

What is the slope of the line ?

Answer

You can rearrange to get an equation resembling the formula by isolating the . This gives you the equation . The slope of the equation is 2 (the within the equation).

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Question

What is the slope of the line ?

Answer

To easily find the slope of the line, you can rearrange the equation to the form. To do this, isolate the by moving the to the other side of the equation. This gives you . Then, divide both sides by 3 to isolate the , which leaves you with . Now, the equation is in the form, and you can easily see that the slope is 3.

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Question

What is the slope of the line depicted by this equation?

$\small 4x+5y=14$

Answer

This equation is written in standard form, that is, $\small Ax+By=C$ where the slope is equal to $\small \frac{-A}{B}$ .

$\small 4x+5y=14$

In this instance $\small A=4$ and $\small B=5$

$m=-\frac{A}{B}=-\frac{4}{5}$

This question can also be solved by converting the slope-intercept form: $\small y=-\frac{4}{5}x+\frac{14}{5}$ .

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Question

Line is a straight line that passes through these points on a graph:(-4,0) (0,3) and (4,6). What is the slope of line ?

Answer

To calculate the slope of a line, we pick two points, and calculate the change in divided by the change in . To calculate the change in value, we use subtraction. So,

slope = $\frac{\text{Change in Y}}{\text{Change in X}} = \frac{y_2-y_1}{x_2-x_1}$

So we can pick any two points and plug them into this formula. Let's choose (0,3) and (4,6). We get

$\frac{6-3}{4-0}= \frac{3}{4}$

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Question

What is the slope of the line depicted by the equation?

Answer

The equation is written in standard from: $\small Ax+By=C$ . In this format, the slope is $\small -\frac{A}{B}$ .

In our equation, $\small A=6$ and $\small B=3$ .

$\small m=-\frac{A}{B}=-\frac{6}{3}$

$\small -\frac{6}{3}=-2$

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Question

Given:

Determine the slope of this line.

Answer

is the standard form for a linear equation.

Given this linear equation, you were asked to determine the slope of the line.

In order to find the slope we have to first put the equation in to slope intercept form, .

Solving for :

Subtract the from both sides, , divide the entire equation by , to isolate

$y = \frac{-ax}{b}+\frac{c}{b}$

The slope then is $-\frac{a}{b}$ .

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Question

Find the slope of the line defined by the equation .

Answer

$- 6y \div (-6)=\left ( -4x + 15 \right )\div (-6)$

$y =\frac{2}{3 }x- \frac{5}{2}$

The slope is the coefficient of : $m = \frac{2}{3}$

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Question

Find the slope of the line defined by the equation .

Answer

Rewrite in slope-intercept form:

$6y \div 6= \left (-2x +15 \right )\div 6$

$y= - \frac{1}{3}x +\frac{5}{2}$

The slope is the coefficient of :

$m = - \frac{1}{3}$

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Question

Find the slope of the line that includes points and .

Answer

Use the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-2-(-4)}{8-5} = \frac{2}{3}$

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Question

Find the slope of the line that includes points and .

Answer

Use the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-2-4}{8-5} = \frac{-6}{3} = -2$

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Question

The following equation describes a straight line.

Identify the slope and y-intercept of the line.

Answer

The general formula of a straight line is , where $\small m$ is the slope and $\small b$ is the y-intercept.

To evaluate our original equation, we can compare it to this formula.

The slope is $\small -2$ and the y-intercept is at $\small -3$ . Since the y-intercept is a point on the line, it is written as $\small (0,-3)$ .

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