How to find the slope of a line - Intermediate Geometry

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Question

What is the slope of the line that passes through the points and ?

Answer

The slope of a line is sometimes referred to as "rise over run." This is because the formula for slope is the change in y-value (rise) divided by the change in x-value (run). Therefore, if you are given two points, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , the slope of their line can be found using the following formula: $slope=(y_{1}-y_{2})/(x_{1}-x_{2})$

This gives us .

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Question

Given the points and , find the slope of the line.

Answer

The formula for the slope of a line is $\frac{y_2-y_1}{x_2-x_1}$ .

We then plug in the points given: $\frac{9-3}{8-4}=\frac{6}{4}$ which is then reduced to $\frac{3}{2}$ .

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Question

Given points and , what is the slope of the line connecting them?

Answer

Write the slope formula. Plug in the points and solve.

$m= \frac{y_2-y_1}{x_2-x_1}= \frac{3-2}{-1-1}= -\frac{1}{2}$

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Question

What is the slope of the line connecting the points $(2,\sqrt2)$ and ?

Answer

Write the slope formula. Plug in the point, and simplify.

$m=\frac{y_2-y_1}{x_2-x_1}= \frac{2-\sqrt2}{1-2}=\frac{2-\sqrt2}{-1}= -(2-\sqrt2) = \sqrt2-2$

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Question

What is the slope of a line with an -intercept is and another -intercept of ?

Answer

The -intercept is the value when .

Therefore, since the two -intercepts are and , the points are and .

Write the slope formula, plug in the values, and solve.

$m=\frac{y_2-y_1}{x_2-x_1} = \frac{0-0}{6-4}= \frac{0}{2} =0$

The slope is zero.

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Question

What is the slope m of the line below?

Answer

To answer this question you should realize that the equation for the line is given in point - slope form. The standard point slope form of a line is given below:

m represents the slope of the line so all we have to do is recognize the correct line form and we automatically know that the slope is

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Question

A line crosses the x-axis at and the y-axis at . What is the slope of this line?

Answer

Given the points,

$\(x_1,y_1)=(0,6) \(x_2,y_2)=(6,8)$ .

We compute slope (m) as follows:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{6-0}=\mathbf{\frac{1}{3}}$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{4-2}{-12-12}$

Simplify.

$\text{Slope}=\frac{2}{-24}$

Solve.

$\text{Slope}=-\frac{1}{12}$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{-20-4}{-10-2}$

Simplify.

$\text{Slope}=\frac{-24}{-12}$

Solve.

$\text{Slope}=2$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{1-5}{-3-4}$

Simplify.

$\text{Slope}=\frac{-4}{-7}$

Solve.

$\text{Slope}=\frac{4}{7}$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{13-15}{-39-8}$

Simplify.

$\text{Slope}=\frac{-2}{-47}$

Solve.

$\text{Slope}=\frac{2}{47}$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{6-(-10)}{5-4}$

Simplify.

$\text{Slope}=\frac{16}{1}$

Solve.

$\text{Slope}=16$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{-16-2}{14-0}$

Simplify.

$\text{Slope}=\frac{-18}{14}$

Solve.

$\text{Slope}=-\frac{9}{7}$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{20-14}{100-92}$

Simplify.

$\text{Slope}=\frac{6}{8}$

Solve.

$\text{Slope}=\frac{3}{4}$

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Question

Find the slope of the line that passes through the points:

and

Answer

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{12-(-14)}{34-(-10)}$

Simplify.

$\text{Slope}=\frac{26}{44}$

Solve.

$\text{Slope}=\frac{13}{22}$

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Question

Give the slope of the line of the equation

Answer

If we divide both sides by 8, as follows:

$\frac{8y}{8} = \frac{1}{8}$

$y = \frac{1}{8}$

we see that the equation is equivalent to one of the form . This is a horizontal line, and its slope is 0.

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Question

Give the slope of the line of the equation $- \frac{2}{3}x = 4$ .

Answer

If we multiply both sides of the equation by $-\frac{3}{2}$ , as follows:

$- \frac{2}{3}x = 4$

$- \frac{3}{2} \cdot \left (- \frac{2}{3}x \right )=- \frac{3}{2} \cdot 4$

we see that the equation is equivalent to one of the form . This is a vertical line, which has undefined slope.

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