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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

What is the slope of the line connecting the points $(2,\sqrt2)$ and (1,2) ?

Possible Answers:

$-\sqrt2+1$

$-1-\sqrt2$

$\sqrt2 -2$

$2-\sqrt2$

$-\sqrt2-2$

Correct answer:

$\sqrt2 -2$

Explanation:

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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Example Question #2 : How To Find The Slope Of A Line

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

Possible Answers:

$\infty$

Correct answer:

Explanation:

The -intercept is the value when y=0 .

Therefore, since the two -intercepts are and , the points are (4,0) and (6,0) .

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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Example Question #2 : How To Find The Slope Of A Line

Given the points (4, 3) and (8, 9) , find the slope of the line.

Possible Answers:

$\frac{4}{3}$

$\frac{-3}{4}$

$\frac{3}{2}$

$\frac{-6}{4}$

$\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

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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Example Question #3 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

A line crosses the x-axis at (6,8) and the y-axis at (0,6) . What is the slope of this line?

Possible Answers:

m=3

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

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

None of these.

m=-3

Correct answer:

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

Explanation:

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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Example Question #4 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

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

(12, 2) and (-12, 4)

Possible Answers:

$-\frac{1}{12}$

$-\frac{3}{4}$

Correct answer:

$-\frac{1}{12}$

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.

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

Simplify.

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

Solve.

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

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Example Question #1 : How To Find The Slope Of A Line

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

(2, 4) and (-10, -20)

Possible Answers:

$-\frac{1}{2}$

$\frac{7}{8}$

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.

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

Simplify.

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

Solve.

$\text{Slope}=2$

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Example Question #6 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

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

(4, 5) and (-3, 1)

Possible Answers:

$\frac{5}{7}$

$-\frac{2}{7}$

$\frac{3}{7}$

$\frac{4}{7}$

Correct answer:

$\frac{4}{7}$

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.

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

Simplify.

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

Solve.

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

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Example Question #7 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

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

(8, 15) and (-39, 13)

Possible Answers:

$\frac{12}{47}$

$\frac{2}{47}$

$-\frac{34}{47}$

$\frac{19}{4}$

Correct answer:

$\frac{2}{47}$

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.

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

Simplify.

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

Solve.

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

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Example Question #1421 : 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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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #2 : How To Find The Slope Of A Line

Example Question #2 : How To Find The Slope Of A Line

Example Question #3 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #4 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #1 : How To Find The Slope Of A Line

Example Question #6 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #7 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #1421 : Intermediate Geometry

Example Question #141 : Coordinate Geometry

All Intermediate Geometry Resources

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