GMAT Math : Calculating the slope of a line

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Example Questions

Example Question #81 : Lines

What is the slope of the line $\displaystyle Ax + 2Ay = 3A$ ?

Possible Answers:

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

$\displaystyle -2$

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

$\frac{A}{2}$ $\displaystyle \frac{A}{2}$

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

Correct answer:

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

Explanation:

Rewrite this equation in slope-intercept form: $\displaystyle y = mx + b$, where $\displaystyle m$ is the slope.

$\displaystyle Ax + 2Ay = 3A$

$\displaystyle 2Ay = - Ax + 3A$

$\frac{2Ay}{2A} = \frac{- Ax + 3A}{2A}$ $\displaystyle \frac{2Ay}{2A} = \frac{- Ax + 3A}{2A}$

$y = -\frac{1}{2}x+ \frac{3}{2}$ $\displaystyle y = -\frac{1}{2}x+ \frac{3}{2}$

The slope is the coefficient of $\displaystyle x$, which is $-\frac{1}{2}$ $\displaystyle -\frac{1}{2}$.

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Example Question #82 : Lines

Give the slope of the line of the equation: $\displaystyle 0.4x - 0.5y = 20$

Possible Answers:

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\displaystyle -2$

$-\frac{5}{4}$ $\displaystyle -\frac{5}{4}$

$-\frac{4}{5}$ $\displaystyle -\frac{4}{5}$

$\frac{5}{4}$ $\displaystyle \frac{5}{4}$

Correct answer:

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

Explanation:

Rewrite in the slope-intercept form $\displaystyle y = mx + b$:

$\displaystyle 0.4x - 0.5y = 20$

$\left (0.4x - 0.5y \right )\cdot 10 = 20 \cdot 10$ $\displaystyle \left (0.4x - 0.5y \right )\cdot 10 = 20 \cdot 10$

$\left (0.4x \right )\cdot 10-\left ( 0.5y \right )\cdot 10 = 200$ $\displaystyle \left (0.4x \right )\cdot 10-\left ( 0.5y \right )\cdot 10 = 200$

$\displaystyle 4x-5y = 200$

$\displaystyle 4x-4x-5y = 200-4x$

$\displaystyle -5y = -4x+ 200$

$-5y \div (-5)=\left ( -4x+ 200 \right )\div (-5)$ $\displaystyle -5y \div (-5)=\left ( -4x+ 200 \right )\div (-5)$

$y=\left ( -4x \right ) \div (-5)+\left ( 200 \right ) \div (-5)$ $\displaystyle y=\left ( -4x \right ) \div (-5)+\left ( 200 \right ) \div (-5)$

$y= \frac{4}{5}x-40$ $\displaystyle y= \frac{4}{5}x-40$

The slope is the coefficient of $\displaystyle x$, which is $\frac{4}{5}$ $\displaystyle \frac{4}{5}$.

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Example Question #3 : Calculating The Slope Of A Line

Give the slope of the line of the equation: $\frac{}{}$ $\displaystyle \frac{}{}$ $\frac{2}{5}x + \frac{6}{7}y = 9$ $\displaystyle \frac{2}{5}x + \frac{6}{7}y = 9$

Possible Answers:

$-\frac{15}{7}$ $\displaystyle -\frac{15}{7}$

$-\frac{7}{15}$ $\displaystyle -\frac{7}{15}$

$\frac{45}{2}$ $\displaystyle \frac{45}{2}$

$\frac{12}{35}$ $\displaystyle \frac{12}{35}$

$\frac{21}{2}$ $\displaystyle \frac{21}{2}$

Correct answer:

$-\frac{7}{15}$ $\displaystyle -\frac{7}{15}$

Explanation:

Rewrite in the slope-intercept form $\displaystyle y = mx + b$:

$\frac{2}{5}x + \frac{6}{7}y = 9$ $\displaystyle \frac{2}{5}x + \frac{6}{7}y = 9$

$\frac{2}{5}x - \frac{2}{5}x + \frac{6}{7}y = - \frac{2}{5}x+ 9$ $\displaystyle \frac{2}{5}x - \frac{2}{5}x + \frac{6}{7}y = - \frac{2}{5}x+ 9$

$\frac{6}{7}y = - \frac{2}{5}x+ 9$ $\displaystyle \frac{6}{7}y = - \frac{2}{5}x+ 9$

$\frac{6}{7}y \cdot \frac{7}{6}=\left ( - \frac{2}{5}x+ 9 \right )\cdot \frac{7}{6}$ $\displaystyle \frac{6}{7}y \cdot \frac{7}{6}=\left ( - \frac{2}{5}x+ 9 \right )\cdot \frac{7}{6}$

$y=- \frac{2}{5}\cdot \frac{7}{6}x+ 9 \cdot \frac{7}{6}$ $\displaystyle y=- \frac{2}{5}\cdot \frac{7}{6}x+ 9 \cdot \frac{7}{6}$

$y=-\frac{7}{15}x+ \frac{21}{2}$ $\displaystyle y=-\frac{7}{15}x+ \frac{21}{2}$

The slope is the coefficient of $\displaystyle x$, which is $-\frac{7}{15}$ $\displaystyle -\frac{7}{15}$

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Example Question #4 : Calculating The Slope Of A Line

Give the slope of the line of the equation

$\displaystyle 5y = x - 7$

Possible Answers:

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

$\displaystyle 5$

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

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

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

Correct answer:

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

Explanation:

Rewrite in the slope-intercept form $\displaystyle y = mx + b$:

$\displaystyle 5y = x - 7$

$\frac{1}{5} \cdot 5y = \frac{1}{5} \cdot \left ( x - 7 \right )$ $\displaystyle \frac{1}{5} \cdot 5y = \frac{1}{5} \cdot \left ( x - 7 \right )$

$y = \frac{1}{5} x - \frac{7}{5} \right )$ $\displaystyle y = \frac{1}{5} x - \frac{7}{5} \right )$

The slope is the coefficient of $\displaystyle x$, or $\frac{1}{5}$ $\displaystyle \frac{1}{5}$.

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Example Question #5 : Calculating The Slope Of A Line

What is the slope of the line that contains (1,4) $\displaystyle (1,4)$ and (7,10) $\displaystyle (7,10)$?

Possible Answers:

$\displaystyle 1$

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

$\frac{14}{8}$ $\displaystyle \frac{14}{8}$

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

Correct answer:

$\displaystyle 1$

Explanation:

The slope formula is:

$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $\displaystyle m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$(1,4)\ and\ (7,10)$ $\displaystyle (1,4)\ and\ (7,10)$

$m= \frac{7-1}{10-4}$ $\displaystyle m= \frac{7-1}{10-4}$

$m= \frac{6}{}6$ $\displaystyle m= \frac{6}{}6$

$\displaystyle m=1$

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Example Question #6 : Calculating The Slope Of A Line

What is the slope of the line that contains (1,2) $\displaystyle (1,2)$ and (5,2) $\displaystyle (5,2)$?

Possible Answers:

$\displaystyle 0$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{6}{4}$ $\displaystyle \frac{6}{4}$

$\frac{4}{6}$ $\displaystyle \frac{4}{6}$

Correct answer:

$\displaystyle 0$

Explanation:

The slope formula is:

$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $\displaystyle m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

$m=\frac{2-2}{5-1}$ $\displaystyle m=\frac{2-2}{5-1}$

$m=\frac{0}{4}$ $\displaystyle m=\frac{0}{4}$

$\displaystyle m=0$

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Example Question #7 : Calculating The Slope Of A Line

What is the slope of the line that contains (-2,-1) $\displaystyle (-2,-1)$ and (-8,7) $\displaystyle (-8,7)$?

Possible Answers:

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

$-\frac{4}{3}$ $\displaystyle -\frac{4}{3}$

$-\frac{3}{4}$ $\displaystyle -\frac{3}{4}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

Correct answer:

$-\frac{4}{3}$ $\displaystyle -\frac{4}{3}$

Explanation:

The slope formula is:

$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $\displaystyle m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$(-2,-1)\ and\ (-8,7)$ $\displaystyle (-2,-1)\ and\ (-8,7)$

$m=\frac{7-(-1)}{-8-(-2)}$ $\displaystyle m=\frac{7-(-1)}{-8-(-2)}$

$m=\frac{7+1}{-8+2}$ $\displaystyle m=\frac{7+1}{-8+2}$

$m=\frac{8}{-6}$ $\displaystyle m=\frac{8}{-6}$

$m=-\frac{4}{3}$ $\displaystyle m=-\frac{4}{3}$

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Example Question #21 : Other Lines

A iine goes through points $\displaystyle (6,N + 4 )$ and $\displaystyle (3,2N + 6)$. What is its slope?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Substitute $\displaystyle x_1= 6 , y_1=N + 4,x_2= 3, y_2 =2N + 6$ in the slope formula:

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

$m = \frac{(2N+6 )- (N+4)}{3-6} = \frac{2N+6 -N-4}{-3}= \frac{N+2}{-3} = \frac{-N-2}{3}$ $\displaystyle m = \frac{(2N+6 )- (N+4)}{3-6} = \frac{2N+6 -N-4}{-3}= \frac{N+2}{-3} = \frac{-N-2}{3}$

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Example Question #1 : Calculating The Slope Of A Line

In the $\displaystyle xy$-plane, what is the slope of the line with equation $4x+5y=8$ $\displaystyle 4x+5y=8$ ?

Possible Answers:

$-\frac{4}{5}$ $\displaystyle -\frac{4}{5}$

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

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

$-4$ $\displaystyle -4$

$4$ $\displaystyle 4$

Correct answer:

$-\frac{4}{5}$ $\displaystyle -\frac{4}{5}$

Explanation:

Put the equation in slope-intercept form to solve for the slope:

$y=mx+b$ $\displaystyle y=mx+b$, where m is the slope and b is the intercept

Rearrange terms: $5y=-4x+8$ $\displaystyle 5y=-4x+8$

Divide by 5: $y=-\frac{4}{5}x+\frac{8}{5}$ $\displaystyle y=-\frac{4}{5}x+\frac{8}{5}$

slope = $-\frac{4}{5}$ $\displaystyle -\frac{4}{5}$

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Example Question #10 : Calculating The Slope Of A Line

Give the slope of the line with the equation $\frac{4}{3} x = \frac{2}{5} y - 10$ $\displaystyle \frac{4}{3} x = \frac{2}{5} y - 10$.

Possible Answers:

$\frac{1}{25}$ $\displaystyle \frac{1}{25}$

$\frac{15}{8}$ $\displaystyle \frac{15}{8}$

$\frac{8}{15}$ $\displaystyle \frac{8}{15}$

$\frac{10}{3}$ $\displaystyle \frac{10}{3}$

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

Correct answer:

$\frac{10}{3}$ $\displaystyle \frac{10}{3}$

Explanation:

Rewrite in slope-intercept form:

$\frac{4}{3} x = \frac{2}{5} y - 10$ $\displaystyle \frac{4}{3} x = \frac{2}{5} y - 10$

$\frac{4}{3} x + 10 = \frac{2}{5} y - 10 + 10$ $\displaystyle \frac{4}{3} x + 10 = \frac{2}{5} y - 10 + 10$

$\frac{2}{5} y = \frac{4}{3} x + 10$ $\displaystyle \frac{2}{5} y = \frac{4}{3} x + 10$

$\frac{5} {2} \cdot \frac{2}{5} y= \frac{5} {2} \cdot \left ( \frac{4}{3} x + 10 \right )$ $\displaystyle \frac{5} {2} \cdot \frac{2}{5} y= \frac{5} {2} \cdot \left ( \frac{4}{3} x + 10 \right )$

$y= \frac{5} {2} \cdot \frac{4}{3} x + \frac{5} {2} \cdot 10$ $\displaystyle y= \frac{5} {2} \cdot \frac{4}{3} x + \frac{5} {2} \cdot 10$

$y= \frac{10}{3} x +25$ $\displaystyle y= \frac{10}{3} x +25$

The slope is the coefficient of $\displaystyle x$, which is $\frac{10}{3}$ $\displaystyle \frac{10}{3}$.

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GMAT Math : Calculating the slope of a line

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #81 : Lines

Example Question #82 : Lines

Example Question #3 : Calculating The Slope Of A Line

Example Question #4 : Calculating The Slope Of A Line

Example Question #5 : Calculating The Slope Of A Line

Example Question #6 : Calculating The Slope Of A Line

Example Question #7 : Calculating The Slope Of A Line

Example Question #21 : Other Lines

Example Question #1 : Calculating The Slope Of A Line

Example Question #10 : Calculating The Slope Of A Line

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