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ACT Math : How to find the slope of a line

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Example Questions

Example Question #111 : Coordinate Geometry

What is the slope of line 3 = 8y - 4x?

Possible Answers:

-2

0.5

-0.5

Correct answer:

0.5

Explanation:

Solve equation for y. y=mx+b, where m is the slope

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Example Question #112 : Coordinate Geometry

If 2x – 4y = 10, what is the slope of the line?

Possible Answers:

–5/2

–2

–0.5

0.5

Correct answer:

0.5

Explanation:

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

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Example Question #113 : Coordinate Geometry

What is the slope of the line with equation 4x – 16y = 24?

Possible Answers:

1/8

–1/8

–1/4

1/2

1/4

Correct answer:

1/4

Explanation:

The equation of a line is:

y = mx + b, where m is the slope

4x – 16y = 24

–16y = –4x + 24

y = (–4x)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

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Example Question #114 : Coordinate Geometry

What is the slope of a line which passes through coordinates $\dpi{100} \small (3,7)$ $\displaystyle \dpi{100} \small (3,7)$ and $\dpi{100} \small (4,12)$ $\displaystyle \dpi{100} \small (4,12)$?

Possible Answers:

$\dpi{100} \small \frac{1}{2}$ $\displaystyle \dpi{100} \small \frac{1}{2}$

$\dpi{100} \small 5$ $\displaystyle \dpi{100} \small 5$

$\dpi{100} \small \frac{1}{5}$ $\displaystyle \dpi{100} \small \frac{1}{5}$

$\dpi{100} \small 3$ $\displaystyle \dpi{100} \small 3$

$\dpi{100} \small 2$ $\displaystyle \dpi{100} \small 2$

Correct answer:

$\dpi{100} \small 5$ $\displaystyle \dpi{100} \small 5$

Explanation:

Slope is found by dividing the difference in the $\dpi{100} \small y$ $\displaystyle \dpi{100} \small y$-coordinates by the difference in the $\dpi{100} \small x$ $\displaystyle \dpi{100} \small x$-coordinates.

$\dpi{100} \small \frac{(12-7)}{(4-3)}=\frac{5}{1}=5$ $\displaystyle \dpi{100} \small \frac{(12-7)}{(4-3)}=\frac{5}{1}=5$

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

What is the slope of the line represented by the equation $6y-16x=7$ $\displaystyle 6y-16x=7$ ?

Possible Answers:

$16$ $\displaystyle 16$

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

$6$ $\displaystyle 6$

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

$-16$ $\displaystyle -16$

Correct answer:

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

Explanation:

To rearrange the equation into a $y=mx+b$ $\displaystyle y=mx+b$ format, you want to isolate the $y$ $\displaystyle y$ so that it is the sole variable, without a coefficient, on one side of the equation.

First, add $11x$ $\displaystyle 11x$ to both sides to get $6y=7+16x$ $\displaystyle 6y=7+16x$ .

Then, divide both sides by 6 to get $y=\frac{7+16x}{6}$ $\displaystyle y=\frac{7+16x}{6}$ .

If you divide each part of the numerator by 6, you get $y=\frac{7}{6}+\frac{16x}{6}$ $\displaystyle y=\frac{7}{6}+\frac{16x}{6}$ . This is in a $y=b+mx$ $\displaystyle y=b+mx$ form, and the $m$ $\displaystyle m$ is equal to $\frac{16}{6}$ $\displaystyle \frac{16}{6}$, which is reduced down to $\frac{8}{3}$ $\displaystyle \frac{8}{3}$ for the correct answer.

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Example Question #115 : Coordinate Geometry

What is the slope of the given linear equation?

2x + 4y = -7

Possible Answers:

-2

1/2

-1/2

-7/2

Correct answer:

-1/2

Explanation:

We can convert the given equation into slope-intercept form, y=mx+b, where m is the slope. We get y = (-1/2)x + (-7/2)

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Example Question #116 : Coordinate Geometry

What is the slope of the line:

$\frac{14}{3}x=\frac{1}{6}y-7$ $\displaystyle \frac{14}{3}x=\frac{1}{6}y-7$

Possible Answers:

$\displaystyle 28$

$\displaystyle -7$

$-\frac{1}{28}$ $\displaystyle -\frac{1}{28}$

$\frac{1}{28}$ $\displaystyle \frac{1}{28}$

$\displaystyle -28$

Correct answer:

$\displaystyle 28$

Explanation:

First put the question in slope intercept form (y = mx + b):

–(1/6)y = –(14/3)x – 7 =>

y = 6(14/3)x – 7

y = 28x – 7.

The slope is 28.

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Example Question #117 : Coordinate Geometry

What is the slope of a line that passes though the coordinates $(5,2)$ $\displaystyle (5,2)$ and $(3,1)$ $\displaystyle (3,1)$?

Possible Answers:

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

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

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

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

$4$ $\displaystyle 4$

Correct answer:

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

Explanation:

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

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

Use the give points in this formula to calculate the slope.

$m=\frac{1-2}{3-5}=\frac{-1}{-2}=\frac{1}{2}$ $\displaystyle m=\frac{1-2}{3-5}=\frac{-1}{-2}=\frac{1}{2}$

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Example Question #118 : Coordinate Geometry

What is the slope of a line running through points (7,3) $\displaystyle (7,3)$ and (8,-4) $\displaystyle (8,-4)$?

Possible Answers:

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

$\displaystyle -7$

$-\frac{1}{7}$ $\displaystyle -\frac{1}{7}$

$\displaystyle 7$

$\displaystyle 1$

Correct answer:

$\displaystyle -7$

Explanation:

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

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

Use the give points in this formula to calculate the slope.

$m=\frac{3-(-4)}{7-8}=\frac{7}{-1}=-7$ $\displaystyle m=\frac{3-(-4)}{7-8}=\frac{7}{-1}=-7$

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Example Question #4 : How To Find The Slope Of A Line

What is the slope of the line defined as $\displaystyle 3x + 4y = 22$?

Possible Answers:

$\frac{-2}{11}$ $\displaystyle \frac{-2}{11}$

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

$\frac{11}{2}$ $\displaystyle \frac{11}{2}$

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

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

Correct answer:

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

Explanation:

$\displaystyle 3x + 4y = 22$

To calculate the slope of a line from an equation of the line, the easiest way to proceed is to solve it for $\displaystyle y$. This will put it into the format y=mx+b $\displaystyle y=mx+b$, making it very easy to find the slope $\displaystyle m$. For our equation, it is:

$\displaystyle 4y = 22-3x$ or $\displaystyle 4y = -3x+22$

Next you merely need to divide by $\displaystyle 4$:

$y = \frac{-3}{4}x+\frac{22}{4}$ $\displaystyle y = \frac{-3}{4}x+\frac{22}{4}$

Thus, the slope is $\frac{-3}{4}$ $\displaystyle \frac{-3}{4}$

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ACT Math : How to find the slope of a line

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #111 : Coordinate Geometry

Example Question #112 : Coordinate Geometry

Example Question #113 : Coordinate Geometry

Example Question #114 : Coordinate Geometry

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

Example Question #115 : Coordinate Geometry

Example Question #116 : Coordinate Geometry

Example Question #117 : Coordinate Geometry

Example Question #118 : Coordinate Geometry

Example Question #4 : How To Find The Slope Of A Line

All ACT Math Resources

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