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Intermediate Geometry : How to find the slope of a line

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1427 : Intermediate Geometry

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

(4, -10) and (5, 6)

Possible Answers:

Correct answer:

Explanation:

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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Example Question #141 : Coordinate Geometry

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

(0, 2) and (14, -16)

Possible Answers:

$-\frac{10}{7}$

$-\frac{9}{7}$

$-\frac{8}{7}$

Correct answer:

$-\frac{9}{7}$

Explanation:

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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Example Question #11 : How To Find The Slope Of A Line

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

(92, 14) and (100, 20)

Possible Answers:

$-\frac{1}{4}$

$\frac{3}{4}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{4}$

Explanation:

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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Example Question #1432 : Intermediate Geometry

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

(-10, -14) and (34, 12)

Possible Answers:

$\frac{1}{2}$

$\frac{13}{22}$

$\frac{5}{11}$

$-\frac{7}{11}$

Correct answer:

$\frac{13}{22}$

Explanation:

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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Example Question #11 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

What is the slope m of the line below?

y - 2= 2(x-4)

Possible Answers:

m = 2

m=4

m=-2

m=-4

m=-8

Correct answer:

m = 2

Explanation:

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:

y-y_1 = m(x-x_1)

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 m = 2

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Example Question #1433 : Intermediate Geometry

Give the slope of the line of the equation 8y = 1

Possible Answers:

$\textup{The slope is undefined}$

$\frac{1}{8}$

Correct answer:

Explanation:

If we divide both sides by 8, as follows:

8y = 1

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

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

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

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Example Question #11 : How To Find The Slope Of A Line

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

Possible Answers:

$\textup{The slope is undefined}$

$- \frac{3}{2}$

$- \frac{2}{3}$

Correct answer:

$\textup{The slope is undefined}$

Explanation:

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

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

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

x = 6

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

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Intermediate Geometry : How to find the slope of a line

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1427 : Intermediate Geometry

Example Question #141 : Coordinate Geometry

Example Question #11 : How To Find The Slope Of A Line

Example Question #1432 : Intermediate Geometry

Example Question #11 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #1433 : Intermediate Geometry

Example Question #11 : How To Find The Slope Of A Line

All Intermediate Geometry Resources

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