SAT Math : How to find x or y intercept

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #596 : Geometry

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

Possible Answers:

5

2

\frac{3}{5}

\pm 5

\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!

Example Question #597 : Geometry

A line with the exquation y=x^2+3x+c passes through the point .  What is the -intercept?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #598 : Geometry

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

Possible Answers:

Correct answer:

Explanation:

We can factor and set  equal to zero to determine the -intercepts.

satisfies this equation.

 

Therefore our -intercepts are  and .

Example Question #599 : Geometry

Which of the following lines does not intersect the line ?

Possible Answers:

Correct answer:

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.

Example Question #600 : Geometry

Find the y-intercept of .

Possible Answers:

3

5

7

12

14

Correct answer:

7

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.

Example Question #601 : Geometry

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

Possible Answers:

(0,4.3)

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

None of the available answers

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

Correct answer:

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}

Example Question #602 : Geometry

Determine the x-intercept for the equation:  

Possible Answers:

Correct answer:

Explanation:

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

The x-intercept is .

Example Question #603 : Geometry

What is the y intercept of 

Possible Answers:

y=12

y=3

The line does not cross the y axis.

y=-3

Correct answer:

y=3

Explanation:

To find the y intercept, substitute x=0

Example Question #604 : Geometry

At what point does the line  intersect the y-axis?

Possible Answers:

None of the given answers

Correct answer:

Explanation:

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

Therefore, when . With this in mind, our y-intercept is 

Example Question #605 : Geometry

Give the area of the triangle on the coordinate plane that is bounded by the -axis, and the lines of the equations  and .

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

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  - and the line of the equation , is found by noting that if , then, by substitution, ; this point of intersection is at , the origin. 

The intersection of the -axis and the line of the equation  is the -intercept of the latter line. Since its equation is written in slope-intercept form , with  the -coordinate of the -intercept, this intercept is .

The intersection of the lines with equations  and  can be found using the substitution method, setting  in the latter equation and solving for :

Since , making  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 . The area is half the product of the two, or

.

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