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Algebra 1 : Functions and Lines

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

Example Questions

Example Question #211 : Equations Of Lines

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

(5, 10) $\displaystyle (5, 10)$ and (0, -5) $\displaystyle (0, -5)$

Possible Answers:

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

$\displaystyle 3$

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

$\displaystyle -3$

Correct answer:

$\displaystyle 3$

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:

$\text{Slope}=\frac{-5-10}{0-5}$ $\displaystyle \text{Slope}=\frac{-5-10}{0-5}$

Simplify.

$\text{Slope}=\frac{-15}{-5}$ $\displaystyle \text{Slope}=\frac{-15}{-5}$

Reduce.

$\text{Slope}=3$ $\displaystyle \text{Slope}=3$

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Example Question #212 : Equations Of Lines

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

(12, 9) $\displaystyle (12, 9)$ and $\displaystyle (-4, -6)$

Possible Answers:

$\frac{16}{15}$ $\displaystyle \frac{16}{15}$

$\frac{15}{16}$ $\displaystyle \frac{15}{16}$

$-\frac{15}{16}$ $\displaystyle -\frac{15}{16}$

$-\frac{16}{15}$ $\displaystyle -\frac{16}{15}$

Correct answer:

$\frac{15}{16}$ $\displaystyle \frac{15}{16}$

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:

$\text{Slope}=\frac{-6-9}{-4-12}$ $\displaystyle \text{Slope}=\frac{-6-9}{-4-12}$

Simplify.

$\text{Slope}=\frac{-15}{-16}$ $\displaystyle \text{Slope}=\frac{-15}{-16}$

Reduce.

$\text{Slope}=\frac{15}{16}$ $\displaystyle \text{Slope}=\frac{15}{16}$

Report an Error

Example Question #122 : Slope And Line Equations

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

$\displaystyle (-1, -2)$ and $\displaystyle (-4, -3)$

Possible Answers:

$\displaystyle -2$

$\displaystyle 3$

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

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

Correct answer:

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

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:

$\text{Slope}=\frac{-3-(-2)}{-4-(-1)}$ $\displaystyle \text{Slope}=\frac{-3-(-2)}{-4-(-1)}$

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

$\text{Slope}=\frac{-3+2}{-4+1}$ $\displaystyle \text{Slope}=\frac{-3+2}{-4+1}$

Simplify.

$\text{Slope}=\frac{-1}{-3}$ $\displaystyle \text{Slope}=\frac{-1}{-3}$

Reduce.

$\text{Slope}=\frac{1}{3}$ $\displaystyle \text{Slope}=\frac{1}{3}$

Report an Error

Example Question #53 : How To Find Slope Of A Line

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

(7, 7) $\displaystyle (7, 7)$ and (11, 7) $\displaystyle (11, 7)$

Possible Answers:

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

$\displaystyle 0$

$\displaystyle -4$

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

Correct answer:

$\displaystyle 0$

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:

$\text{Slope}=\frac{7-7}{11-7}$ $\displaystyle \text{Slope}=\frac{7-7}{11-7}$

Simplify.

$\text{Slope}=\frac{0}{4}$ $\displaystyle \text{Slope}=\frac{0}{4}$

Reduce.

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

Report an Error

Example Question #123 : Slope And Line Equations

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

(8, -4) $\displaystyle (8, -4)$ and (8, 0) $\displaystyle (8, 0)$

Possible Answers:

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

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

$\displaystyle 0$

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

Correct answer:

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

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:

$\text{Slope}=\frac{0-(-4)}{8-8}$ $\displaystyle \text{Slope}=\frac{0-(-4)}{8-8}$

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

$\text{Slope}=\frac{0+4}{8-8}$ $\displaystyle \text{Slope}=\frac{0+4}{8-8}$

Simplify.

$\text{Slope}=\frac{4}{0}$ $\displaystyle \text{Slope}=\frac{4}{0}$

Since you cannot divide by $\displaystyle 0$ , the slope of vertical lines are always undefined.

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Example Question #124 : Slope And Line Equations

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

$\displaystyle (-2, -4)$ and (10, 8) $\displaystyle (10, 8)$

Possible Answers:

$\displaystyle 2$

$\displaystyle 4$

$\displaystyle 1$

$\displaystyle -1$

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:

$\text{Slope}=\frac{8-(-4)}{10-(-2)}$ $\displaystyle \text{Slope}=\frac{8-(-4)}{10-(-2)}$

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

$\text{Slope}=\frac{8+4}{10+2}$ $\displaystyle \text{Slope}=\frac{8+4}{10+2}$

Simplify.

$\text{Slope}=\frac{12}{12}$ $\displaystyle \text{Slope}=\frac{12}{12}$

Reduce.

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

Report an Error

Example Question #125 : Slope And Line Equations

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

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

Possible Answers:

$\displaystyle 8$

$\displaystyle 0$

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

$\displaystyle -6$

Correct answer:

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

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:

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

Simplify.

$\text{Slope}=\frac{6}{0}$ $\displaystyle \text{Slope}=\frac{6}{0}$

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

Report an Error

Example Question #131 : Slope And Line Equations

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

(2, 0) $\displaystyle (2, 0)$ and (5, 27) $\displaystyle (5, 27)$

Possible Answers:

$\frac{1}{9}$ $\displaystyle \frac{1}{9}$

$\displaystyle -9$

$\frac{29}{5}$ $\displaystyle \frac{29}{5}$

$\displaystyle 9$

Correct answer:

$\displaystyle 9$

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:

$\text{Slope}=\frac{27-0}{5-2}$ $\displaystyle \text{Slope}=\frac{27-0}{5-2}$

Simplify.

$\text{Slope}=\frac{27}{3}$ $\displaystyle \text{Slope}=\frac{27}{3}$

Reduce.

$\text{Slope}=9$ $\displaystyle \text{Slope}=9$

Report an Error

Example Question #132 : Slope And Line Equations

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

$\displaystyle (-6, -8)$ and (5, 25) $\displaystyle (5, 25)$

Possible Answers:

$\displaystyle 3$

$-\frac{13}{31}$ $\displaystyle -\frac{13}{31}$

$\frac{17}{11}$ $\displaystyle \frac{17}{11}$

$\frac{11}{33}$ $\displaystyle \frac{11}{33}$

Correct answer:

$\displaystyle 3$

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:

$\text{Slope}=\frac{25-(-8)}{5-(-6)}$ $\displaystyle \text{Slope}=\frac{25-(-8)}{5-(-6)}$

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

$\text{Slope}=\frac{25+8}{5+6}$ $\displaystyle \text{Slope}=\frac{25+8}{5+6}$

Simplify.

$\text{Slope}=\frac{33}{11}$ $\displaystyle \text{Slope}=\frac{33}{11}$

Reduce.

$\text{Slope}=3$ $\displaystyle \text{Slope}=3$

Report an Error

Example Question #133 : Slope And Line Equations

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

$\displaystyle (-17, 21)$ and $\displaystyle (-5, -3)$

Possible Answers:

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

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

$\displaystyle 3$

$\displaystyle -2$

Correct answer:

$\displaystyle -2$

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:

$\text{Slope}=\frac{-3-21}{-5-(-17)}$ $\displaystyle \text{Slope}=\frac{-3-21}{-5-(-17)}$

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

$\text{Slope}=\frac{-3-21}{-5+17}$ $\displaystyle \text{Slope}=\frac{-3-21}{-5+17}$

Simplify.

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

Reduce.

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

Report an Error

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #211 : Equations Of Lines

Example Question #212 : Equations Of Lines

Example Question #122 : Slope And Line Equations

Example Question #53 : How To Find Slope Of A Line

Example Question #123 : Slope And Line Equations

Example Question #124 : Slope And Line Equations

Example Question #125 : Slope And Line Equations

Example Question #131 : Slope And Line Equations

Example Question #132 : Slope And Line Equations

Example Question #133 : Slope And Line Equations

All Algebra 1 Resources

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