ACT Math : How to find the slope of a line

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #721 : Act Math

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

Possible Answers:

-0.5

0.5

2

-2

Correct answer:

0.5

Explanation:

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

Example Question #5 : How To Find The Slope Of A Line

Find the slope of the line  6X – 2Y = 14

 

Possible Answers:

-6

-3

3

12

Correct answer:

3

Explanation:

Put the equation in slope-intercept form:

y = mx + c

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

 

Example Question #6 : How To Find The Slope Of A Line

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

Possible Answers:

–5/2

–0.5

2

0.5

–2

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.

Example Question #82 : Lines

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

Possible Answers:

–1/8

–1/4

1/4

1/8

1/2

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

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

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

Possible Answers:

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

\dpi{100} \small 3

\dpi{100} \small 2

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

\dpi{100} \small 5

Correct answer:

\dpi{100} \small 5

Explanation:

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

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

Example Question #34 : Coordinate Geometry

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

Possible Answers:

\frac{8}{3}

\frac{7}{6}

6

-16

16

Correct answer:

\frac{8}{3}

Explanation:

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

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

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

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

Example Question #24 : Other Lines

What is the slope of the given linear equation?

2x + 4y = -7

Possible Answers:

-1/2

1/2

-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)

Example Question #22 : Other Lines

What is the slope of the line:

 

Possible Answers:

Correct answer:

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.

Example Question #23 : Other Lines

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

Possible Answers:

\frac{2}{3}

4

-\frac{2}{3}

\frac{1}{2}

-\frac{1}{2}

Correct answer:

\frac{1}{2}

Explanation:

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

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

Example Question #502 : Geometry

What is the slope of a line running through points and ?

Possible Answers:

Correct answer:

Explanation:

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

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

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