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SAT Math : Geometry

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Example Questions

Example Question #21 : Other Lines

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

Possible Answers:

–1/4

1/2

1/8

1/4

–1/8

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 #3 : Other Lines

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

Possible Answers:

$\dpi{100} \small 3$

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

$\dpi{100} \small 2$

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

$\dpi{100} \small 5$

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.

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

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

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

Possible Answers:

$16$

$-16$

$\frac{8}{3}$

$6$

$\frac{7}{6}$

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.

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Example Question #222 : 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 #231 : Geometry

What is the slope of the line:

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

Possible Answers:

$-\frac{1}{28}$

$\frac{1}{28}$

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.

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Example Question #12 : How To Find Slope Of A Line

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

Possible Answers:

$4$

$-\frac{2}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

$-\frac{1}{2}$

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.

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

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

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

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Example Question #13 : How To Find Slope Of A Line

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

Possible Answers:

$\frac{7}{3}$

$-\frac{1}{7}$

Correct answer:

Explanation:

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

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

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

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

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Example Question #508 : Geometry

Solve each problem and decide which is the best of the choices given.

Find the slope of the line for the given equation.
12x+3y=-6

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{2}$

Correct answer:

Explanation:

For this problem, you have to solve for . We want to get the equation in slope-intercept form,

y=mx+b where represents the slope of the line.

12x+3y=-6

First subtract 12x from each side to get

3y=-12x-6 .

Then divide both sides by to get

y=-4x-2 .

The slope is the number in front of , so the slope is .

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Example Question #504 : Geometry

Point is at (-2,-5) and point is at (3,1) . What is the slope of the line that connects the two points?

Possible Answers:

$\frac{6}{5}$

$-\frac{2}{3}$

$\frac{3}{2}$

$\frac{1}{5}$

$-\frac{6}{5}$

Correct answer:

$\frac{6}{5}$

Explanation:

The purpose of this question is to understand how the slope of a line is calculated.

The slope is the rise over the run, meaning the change in the y values over the change in the x values

$\frac{y_2-y_1}{x_2-x_1}$ .

So, the difference in y values divided by the difference in x values yields

$\frac{1-(-5)}{3-(-2)}=\frac{6}{5}$ .

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Example Question #510 : Geometry

The following two points are located on the same line. What is the slope of the line?

$(2\pi, 5\pi), (11\pi, 6\pi)$

Possible Answers:

$9\pi$

$\frac{1}{9}$

$\frac{1}{9}\pi$

Correct answer:

$\frac{1}{9}$

Explanation:

The slope of a line with two points (x_1, y_1) and (x_2, y_2) is given by the following equation:

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

Let $(x_1, y_1) = (2\pi, 5\pi)$ and $(x_2, y_2) = (11\pi, 6\pi)$ . Substituting these values into the equation gives us:

$m = \frac{6\pi - 5\pi}{11\pi - 2\pi} = \frac{\pi}{9\pi} = \frac{1}{9}$

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SAT Math : Geometry

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : Other Lines

Example Question #3 : Other Lines

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

Example Question #222 : Geometry

Example Question #231 : Geometry

Example Question #12 : How To Find Slope Of A Line

Example Question #13 : How To Find Slope Of A Line

Example Question #508 : Geometry

Example Question #504 : Geometry

Example Question #510 : Geometry

All SAT Math Resources

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