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SAT Math : How to find x or y intercept

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Example Questions

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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Example Question #11 : X And Y Intercept

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

y=x^2+12x+27

Possible Answers:

x=-3,-9

x=27,1

x=3,9

x=3,-9

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 #171 : Coordinate Geometry

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

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 #173 : Geometry

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

Possible Answers:

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

None of the available answers

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

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

$(0,4.3)$

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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Example Question #21 : X And Y Intercept

Determine the x-intercept for the equation: y=3x+9

Possible Answers:

$\frac{1}{3}$

$-\frac{1}{9}$

Correct answer:

Explanation:

The x-intercept is the x-value when the value of y=0 . Substitute this value and solve for .

0=3x+9

-9=3x

$x=\frac{-9}{3}=-3$

The x-intercept is .

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

What is the y intercept of y=12x+3?

Possible Answers:

y=12

$x=\frac{-3}{12}$

The line does not cross the y axis.

y=-3

y=3

Correct answer:

y=3

Explanation:

To find the y intercept, substitute x=0

y=12(0)+3

y=3

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Example Question #15 : How To Find X Or Y Intercept

At what point does the line $\pi x + \frac{\pi}{2}y - 2\pi = 0$ intersect the y-axis?

Possible Answers:

(0.5, 0.5)

None of the given answers

(0, 4)

$(\pi, \frac{1}{2}\pi)$

$(\pi, \pi)$

Correct answer:

(0, 4)

Explanation:

We know that in slope-intercept form, y=mx+b , that represents the y-intercept. So, let's rewrite this line and put it in slope-intercept form.

$\pi x + \frac{\pi}{2}y - 2\pi = 0$

$\frac{\pi}{2}y = -\pi x + 2\pi$

$y = \frac{2}{\pi}(-\pi x+2\pi)$

y = -2x +4

Therefore, when x=0 , y=4 . With this in mind, our y-intercept is (0, 4) .

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Example Question #16 : How To Find X Or Y Intercept

Give the area of the triangle on the coordinate plane that is bounded by the -axis, and the lines of the equations y = x and $y = -\frac{4}{3} x + 3$ .

Possible Answers:

$5\frac{11}{14}$

$3 \frac{6}{7}$

$1 \frac{13}{14}$

$2 \frac{25}{28}$

None of the other choices gives the correct response.

Correct answer:

$1 \frac{13}{14}$

Explanation:

It is necessary to find the vertices of the triangle, which can be done by finding the three points at which two of the three lines intersect.

The intersection of the -axis - the line x = 0 - and the line of the equation y = x , is found by noting that if x = 0 , then, by substitution, y = 0 ; this point of intersection is at (0,0) , the origin.

The intersection of the -axis and the line of the equation $y = -\frac{4}{3} x + 3$ is the -intercept of the latter line. Since its equation is written in slope-intercept form y = mx+b , with the -coordinate of the -intercept, this intercept is (0, 3) .

The intersection of the lines with equations y = x and $y = -\frac{4}{3} x + 3$ can be found using the substitution method, setting y = x in the latter equation and solving for :

$x = -\frac{4}{3} x + 3$

$x+ \frac{4}{3} x= -\frac{4}{3} x + 3 + \frac{4}{3} x$

$\frac{7}{3} x=3$

$\frac{3} {7} \cdot \frac{7}{3} x= \frac{3} {7} \cdot 3$

$x= \frac{9} {7} =1\frac{2}{7}$

Since y = x , $y =1\frac{2}{7}$ , making $\left ( 1\frac{2}{7}, 1\frac{2}{7} \right )$ the point of intersection.

The lines in question are graphed below, and the triangle they bound is shaded:

Triangle z

If we take the vertical side as the base, its length is seen to be 3; the height is the horizontal distance to the opposite vertex, which is its -coordinate $1 \frac{2}{7}$ . The area is half the product of the two, or

$A = \frac{1}{2} \cdot 3 \cdot 1 \frac{2}{7} = 1 \frac{13}{14}$ .

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SAT Math : How to find x or y intercept

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #162 : Geometry

Example Question #163 : Geometry

Example Question #11 : X And Y Intercept

Example Question #171 : Coordinate Geometry

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

Example Question #173 : Geometry

Example Question #21 : X And Y Intercept

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

Example Question #15 : How To Find X Or Y Intercept

Example Question #16 : How To Find X Or Y Intercept

All SAT Math Resources

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