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PSAT Math : How to find x or y intercept

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Example Questions

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

Determine the y-intercept of the following line:

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

Possible Answers:

$\dpi{100} \small 6$

$\dpi{100} \small 1.5$

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

$\dpi{100} \small 3$

$\dpi{100} \small 9$

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 #2 : How To Find X Or Y Intercept

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

Possible Answers:

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

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

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

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

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

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 #11 : X And Y Intercept

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

Possible Answers:

$\frac{3}{5}$

$\pm 5$

$5$

$2$

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

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 #161 : Coordinate 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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Example Question #11 : How To Find X Or Y Intercept

What are the -intercept(s) of the following line:

y=x^2+12x+27

Possible Answers:

x=-3,9

x=3,9

x=3,-9

x=27,1

x=-3,-9

Correct answer:

x=-3,-9

Explanation:

We can factor y=x^2+12x+27 and set equal to zero to determine the -intercepts.

y=(x+3)(x+9) satisfies this equation.

Therefore our -intercepts are and .

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Example Question #12 : How To Find X Or Y Intercept

Which of the following lines does not intersect the line 4x + y = 7 ?

Possible Answers:

$y=-\frac{1}{4}x+11$

y = -4x + 5

y=4x-7

$y=\frac{1}{4}x-7$

y = 4x + 7

Correct answer:

y = -4x + 5

Explanation:

Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in y = –4x + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.

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Example Question #11 : How To Find X Or Y Intercept

Where does the line given by $y=3(x-4)-9$ intercept the -axis?

Possible Answers:

$\frac{4}{3}$

Correct answer:

Explanation:

First, put in slope-intercept form.

y = 3x-12-9

$y=3x-21$ .

To find the -intercept, set y=0 and solve for .

0=3x-21

3x=21

x=7

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Example Question #13 : How To Find X Or Y Intercept

Find the y-intercept of y = 3x^2 +2x + 7 .

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept, set x equal to zero and solve for y.

This gives y = 3(0)² + 2(0) +7 = 7.

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Example Question #14 : How To Find X Or Y Intercept

The slope of a line is $m=\frac{4}{3}$ . The line passes through $(2,7)$ . What is the x-intercept?

Possible Answers:

$(0,9\frac{2}{3})$

$(4\frac{1}{3},0)$

$(0,4.3)$

$\left ( -3\frac{1}{4},0\right )$

None of the available answers

Correct answer:

$\left ( -3\frac{1}{4},0\right )$

Explanation:

The equation for a line is:

$y=mx+b$ , or in this case

$y=\frac{4}{3}x+b$

We can solve for $b$ by plugging in the values given

$7=\frac{4}{3}\times 2+b$

$7=2\frac{2}{3}+b$

$b=7-2\frac{2}{3}=4\frac{1}{3}$

Our line is now

$y=\frac{4}{3}x+4\frac{1}{3}$

Our x-intercept occurs when $\dpi{100} y=0$ , so plugging in and solving for $\dpi{100} x$ :

$\dpi{100} 0=\frac{4}{3}x+4\frac{1}{3}$

$\dpi{100} -\frac{13}{3}=\frac{4}{3}x$

$\dpi{100} x=-\frac{13}{4}$

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PSAT Math : How to find x or y intercept

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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

Example Question #2 : How To Find X Or Y Intercept

Example Question #11 : X And Y Intercept

Example Question #161 : Coordinate Geometry

Example Question #11 : How To Find X Or Y Intercept

Example Question #12 : How To Find X Or Y Intercept

Example Question #11 : How To Find X Or Y Intercept

Example Question #13 : How To Find X Or Y Intercept

Example Question #14 : How To Find X Or Y Intercept

All PSAT Math Resources

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