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Algebra 1 : Slope and Line Equations

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #471 : Functions And Lines

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

(-1, 5) $\displaystyle (-1, 5)$ and (5, -1) $\displaystyle (5, -1)$

Possible Answers:

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\displaystyle 1$

$\displaystyle 5$

$\displaystyle -1$

Correct answer:

$\displaystyle -1$

Explanation:

Use the following formula to find the slope:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

Substitute using the given points:

$\text{Slope}=\frac{-1-5}{5-(-1)}$ $\displaystyle \text{Slope}=\frac{-1-5}{5-(-1)}$

Remember that subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{-1-5}{5+1}$ $\displaystyle \text{Slope}=\frac{-1-5}{5+1}$

Simplify.

$\text{Slope}=\frac{-6}{6}$ $\displaystyle \text{Slope}=\frac{-6}{6}$

Reduce.

$\text{Slope}=-1$ $\displaystyle \text{Slope}=-1$

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Example Question #71 : How To Find Slope Of A Line

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

(-4, 3) $\displaystyle (-4, 3)$ and (3, 3) $\displaystyle (3, 3)$

Possible Answers:

$\frac{6}{7}$ $\displaystyle \frac{6}{7}$

$\frac{7}{5}$ $\displaystyle \frac{7}{5}$

$\displaystyle 0$

$\text{Undefined}$ $\displaystyle \text{Undefined}$

Correct answer:

$\displaystyle 0$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{3-3}{3-(-4)}$ $\displaystyle \text{Slope}=\frac{3-3}{3-(-4)}$

Subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{3-3}{3+4}$ $\displaystyle \text{Slope}=\frac{3-3}{3+4}$

$\text{Slope}=\frac{0}{7}$ $\displaystyle \text{Slope}=\frac{0}{7}$

Simplify.

$\text{Slope}=0$ $\displaystyle \text{Slope}=0$

Report an Error

Example Question #141 : Slope And Line Equations

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

(-1, 4) $\displaystyle (-1, 4)$ and $\displaystyle (-2, -2)$

Possible Answers:

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\displaystyle 6$

$\displaystyle -3$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Correct answer:

$\displaystyle 6$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{-2-4}{-2-(-1)}$ $\displaystyle \text{Slope}=\frac{-2-4}{-2-(-1)}$

Subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{-2-4}{-2+1}$ $\displaystyle \text{Slope}=\frac{-2-4}{-2+1}$

$\text{Slope}=\frac{-6}{-1}$ $\displaystyle \text{Slope}=\frac{-6}{-1}$

Simplify.

$\text{Slope}=6$ $\displaystyle \text{Slope}=6$

Report an Error

Example Question #142 : Slope And Line Equations

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

(-1, 2) $\displaystyle (-1, 2)$ and (5, 7) $\displaystyle (5, 7)$

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{5}{6}$ $\displaystyle \frac{5}{6}$

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

$\displaystyle -2$

Correct answer:

$\frac{5}{6}$ $\displaystyle \frac{5}{6}$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{7-2}{5-(-1)}$ $\displaystyle \text{Slope}=\frac{7-2}{5-(-1)}$

Subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{7-2}{5+1}$ $\displaystyle \text{Slope}=\frac{7-2}{5+1}$

$\text{Slope}=\frac{5}{6}$ $\displaystyle \text{Slope}=\frac{5}{6}$

Report an Error

Example Question #143 : Slope And Line Equations

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

(7, 2) $\displaystyle (7, 2)$ and (5, 1) $\displaystyle (5, 1)$

Possible Answers:

$\displaystyle 4$

$-\frac{1}{3}$ $\displaystyle -\frac{1}{3}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle -2$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{1-2}{5-7}$ $\displaystyle \text{Slope}=\frac{1-2}{5-7}$

$\text{Slope}=\frac{-1}{-2}$ $\displaystyle \text{Slope}=\frac{-1}{-2}$

Simplify.

$\text{Slope}=\frac{1}{2}$ $\displaystyle \text{Slope}=\frac{1}{2}$

Report an Error

Example Question #144 : Slope And Line Equations

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

(8, 0) $\displaystyle (8, 0)$ and (5, 7) $\displaystyle (5, 7)$

Possible Answers:

$-\frac{7}{3}$ $\displaystyle -\frac{7}{3}$

$\frac{3}{7}$ $\displaystyle \frac{3}{7}$

$\frac{7}{13}$ $\displaystyle \frac{7}{13}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Correct answer:

$-\frac{7}{3}$ $\displaystyle -\frac{7}{3}$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{7-0}{5-8}$ $\displaystyle \text{Slope}=\frac{7-0}{5-8}$

$\text{Slope}=\frac{7}{-3}$ $\displaystyle \text{Slope}=\frac{7}{-3}$

Simplify.

$\text{Slope}=-\frac{7}{3}$ $\displaystyle \text{Slope}=-\frac{7}{3}$

Report an Error

Example Question #3767 : Algebra 1

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

(12, 1) $\displaystyle (12, 1)$ and (11, 0) $\displaystyle (11, 0)$

Possible Answers:

$-\frac{13}{2}$ $\displaystyle -\frac{13}{2}$

$\displaystyle 1$

$\displaystyle -1$

$\frac{1}{11}$ $\displaystyle \frac{1}{11}$

Correct answer:

$\displaystyle 1$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{0-1}{11-12}$ $\displaystyle \text{Slope}=\frac{0-1}{11-12}$

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

Simplify.

$\text{Slope}=1$ $\displaystyle \text{Slope}=1$

Report an Error

Example Question #145 : Slope And Line Equations

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

$\displaystyle (-2, -2)$ and (-3, 6) $\displaystyle (-3, 6)$

Possible Answers:

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$-\frac{2}{3}$ $\displaystyle -\frac{2}{3}$

$\displaystyle -8$

Correct answer:

$\displaystyle -8$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{6-(-2)}{-3-(-2)}$ $\displaystyle \text{Slope}=\frac{6-(-2)}{-3-(-2)}$

Subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{6+2}{-3+2}$ $\displaystyle \text{Slope}=\frac{6+2}{-3+2}$

$\text{Slope}=\frac{8}{-1}$ $\displaystyle \text{Slope}=\frac{8}{-1}$

Simplify.

$\text{Slope}=-8$ $\displaystyle \text{Slope}=-8$

Report an Error

Example Question #71 : How To Find Slope Of A Line

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

$\displaystyle (-10, 12)$ and $\displaystyle (-10, -10)$

Possible Answers:

$\text{Undefined}$ $\displaystyle \text{Undefined}$

$\frac{5}{6}$ $\displaystyle \frac{5}{6}$

$\displaystyle 0$

$\frac{11}{5}$ $\displaystyle \frac{11}{5}$

Correct answer:

$\text{Undefined}$ $\displaystyle \text{Undefined}$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

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

Subtracting a negative number is the same as adding a positive number.

$\text{Slope}=\frac{-10-12}{-10+10}$ $\displaystyle \text{Slope}=\frac{-10-12}{-10+10}$

$\text{Slope}=\frac{-22}{0}$ $\displaystyle \text{Slope}=\frac{-22}{0}$

Since you cannot divide by $\displaystyle 0$, the slope of this vertical line is undefined.

Report an Error

Example Question #146 : Slope And Line Equations

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

(5, 7) $\displaystyle (5, 7)$ and (6, 9) $\displaystyle (6, 9)$

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\displaystyle 2$

$\displaystyle 3$

Correct answer:

$\displaystyle 2$

Explanation:

Use the following formula to find the slope of the line:

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

Remember that points are written in the following format:

(x,y) $\displaystyle (x,y)$

For this line,

$\text{Slope}=\frac{9-7}{6-5}$ $\displaystyle \text{Slope}=\frac{9-7}{6-5}$

$\text{Slope}=\frac{2}{1}$ $\displaystyle \text{Slope}=\frac{2}{1}$

Simplify.

$\text{Slope}=2$ $\displaystyle \text{Slope}=2$

Report an Error

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Algebra 1 : Slope and Line Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #471 : Functions And Lines

Example Question #71 : How To Find Slope Of A Line

Example Question #141 : Slope And Line Equations

Example Question #142 : Slope And Line Equations

Example Question #143 : Slope And Line Equations

Example Question #144 : Slope And Line Equations

Example Question #3767 : Algebra 1

Example Question #145 : Slope And Line Equations

Example Question #71 : How To Find Slope Of A Line

Example Question #146 : Slope And Line Equations

All Algebra 1 Resources

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