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SAT Math : Coordinate Geometry

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Example Questions

Example Question #1 : How To Find X Or Y Intercept

If these three points are on a single line, what is the formula for the line?

(3,3)

(4,7)

(5,11)

Possible Answers:

y = 4x - 9

y = 5x + 11

y = 3x - 9

y = 4x + 31

y = 3x - 3

Correct answer:

y = 4x - 9

Explanation:

Formula for a line: y = mx + b

First find slope from two of the points: (3,3) and (4,7)

m = slope = (y2 – y1) / x2 – x1) = (7-3) / (4-3) = 4 / 1 = 4

Solve for b by plugging m and one set of coordinates into the formula for a line:

y = mx + b

11 = 4 * 5 + b

11 = 20 + b

b = -9

y = 4x - 9

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Example Question #1 : X And Y Intercept

The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?

Possible Answers:

(8,15)

(16, 10)

(0,10)

(32,30)

(32,10)

Correct answer:

(32,10)

Explanation:

y = mx + b

x intercept is 16 therefore one coordinate is (16,0)

0 = 5/8 * 16 + b

0 = 10 + b

b = -10

y = 5/8 x – 10

if x = 32

y = 5/8 * 32 – 10 = 20 – 10 = 10

Therefore (32,10)

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Example Question #4 : How To Find X Or Y Intercept

A line has the equation: x+y=1.

What is the y-intercept?

Possible Answers:

0.5

-1

Correct answer:

Explanation:

x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.

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Example Question #5 : How To Find X Or Y Intercept

A line has the equation: 2x+4y=8.

What is the x-intercept?

Possible Answers:

-8

-4

Correct answer:

Explanation:

To find the x-intercept, rearrange the equation 2x+4y=8 so that x is isolated:

2x=-4y+8

x=-2y+4

Using the point-slope formula, we see that the x-intercept is 4.

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Example Question #6 : How To Find X Or Y Intercept

What is the y intercept of the following function of x?

y = 3x

Possible Answers:

–3

–1

Correct answer:

Explanation:

The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.

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Example Question #3 : How To Find X Or Y Intercept

What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?

Possible Answers:

(–3.5, 0)

(0, –0.7)

(0.7, 0)

(–0.7, 0)

(3.5, 0)

Correct answer:

(–0.7, 0)

Explanation:

To solve this, first find the equation of our line. The form of the question gives it to us very directly. We can use the slope-intercept form (y = mx + b).

y = 5x + 3.5

The x-intercept is found by setting y = 0, because that will give us the x-value at which the line crosses the x-axis.

0 = 5x + 3.5; –3.5 = 5x; x = –3.5 / 5 or –0.7. The point will be (–0.7, 0)

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Example Question #4 : How To Find X Or Y Intercept

Determine the y-intercept of the following line:

$\dpi{100} \small 3x+6y=9$

Possible Answers:

$\dpi{100} \small 9$

$\dpi{100} \small 6$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small 1.5$

$\dpi{100} \small 3$

Correct answer:

$\dpi{100} \small 1.5$

Explanation:

The y-intercept occurs when $\dpi{100} \small x=0$

$\dpi{100} \small 3x+6y=9$

$\dpi{100} \small 3(0)+6y=9$

$\dpi{100} \small 0+6y=9$

$\dpi{100} \small y = \frac{9}{6}=1.5$

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Example Question #161 : Psat Mathematics

At what point does the graph $3y-2x=31$ cross the -axis?

Possible Answers:

$\left ( 0,\frac{31}{3} \right )$

$\left ( 0,\frac{2}{3} \right )$

$\left ( 0,-\frac{2}{3} \right )$

$\left ( 0,\frac{3}{31} \right )$

$\left ( 0,\frac{3}{2} \right )$

Correct answer:

$\left ( 0,\frac{31}{3} \right )$

Explanation:

The graph crosses the -axis where $x=0$ . So plugging in and solving yields $\frac{31}{3}$ .

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Example Question #162 : Geometry

Find the x-intercepts of $25x^{2}+4y^{2} = 9$ .

Possible Answers:

$\pm 5$

$5$

$\frac{3}{5}$

$2$

$\pm \frac{3}{5}$

Correct answer:

$\pm \frac{3}{5}$

Explanation:

To find the x-intercepts, plug $y=0$ into the equation and solve for $x$ .

$25x^{2} + 4\cdot 0^{2} = 9$

$25x^{2} = 9$

$x^{2} = \frac{9}{25}$

$x = \pm \frac{3}{5}$

Don't forget that there are two solutions, both negative and positive!

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Example Question #163 : Geometry

A line with the exquation $y=x^2+3x+c$ passes through the point (-4,6) . What is the -intercept?

Possible Answers:

Correct answer:

Explanation:

By plugging in the coordinate, we can figure out that c=2 . The -Intercept is when x=0 , plugging in 0 for gives us y=2 .

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SAT Math : Coordinate Geometry

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Find X Or Y Intercept

Example Question #1 : X And Y Intercept

Example Question #4 : How To Find X Or Y Intercept

Example Question #5 : How To Find X Or Y Intercept

Example Question #6 : How To Find X Or Y Intercept

Example Question #3 : How To Find X Or Y Intercept

Example Question #4 : How To Find X Or Y Intercept

Example Question #161 : Psat Mathematics

Example Question #162 : Geometry

Example Question #163 : Geometry

All SAT Math Resources

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