Intermediate Geometry : How to find x or y intercept

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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

Given the line what is the sum of the and intercepts?

Possible Answers:

Correct answer:

Explanation:

The intercepts cross an axis. 

For the intercept, set to get

For the intercept, set to get

So the sum of the intercepts is .

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

What are the  and -intercepts of the line defined by the equation:

Possible Answers:

Correct answer:

Explanation:

To find the intercepts of a line, we must set the  and  values equal to zero and then solve.  

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

What is the -intercept of the following line:

Possible Answers:

Correct answer:

Explanation:

The -intercept is the point where the y-value is equal to 0. Therefore,

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

Which of the following statements regarding the x and y intercepts of the equation  is true?

Possible Answers:

The x-intercept is greater than the y-intercept.

The x and y intercepts are equal.

The y-intercept is greater than the x-intercept.

The graph does not cross the y-axis.

The graph does not cross the x-axis.

Correct answer:

The y-intercept is greater than the x-intercept.

Explanation:

To find the x-intercept, we simply plug  into our function. giving us . We can factor that equation, making it . We can not solve for , and we get . To find the y-intercept, we do the same thing, however this time, we plug in  instead. This leaves us with . With an x-intercept of  and a y-intercept of , it is clear that the y-intercept is greater than the x-intercept.

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

Find the -intercept of the following function.

Possible Answers:

DNE

Correct answer:

Explanation:

To find the x-intercept, set y equal to 0.

Now solve for x by dividing by 3 on both sides.

This reduces to,

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

Find the -intercept of the following function.

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept, set x equal to 0.

Now solve for y.

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

Which is the x-intercept for the line ?

Possible Answers:

Correct answer:

Explanation:

The x-intercept of a line is the x-value where the line hits the x-axis. This occurs when y is 0. To determine the x-value, plug in 0 for y in the original equation, then solve for x:

add 5 to both sides

divide by 2

Example Question #7 : How To Find X Or Y Intercept

Find the x-intercept(s) for the circle

Possible Answers:

The circle never intersects the x-axis

Correct answer:

Explanation:

The x-intercepts of any curve are the x-values where the curve is intersecting the x-axis. This happens when y = 0. To figure out these x-values, plug in 0 for y in the original equation and solve for x:

adding 0 or 0 square doesn't change the value

take the square root of both sides

this means there are two different potential values for x, and we will have to solve for both. First:

add 4 to both sides

Second: again, add 4 to both sides

Our two answers are and .

Example Question #8 : How To Find X Or Y Intercept

Give the coordinate pair(s) where  intersects with the y-axis.

Possible Answers:

and

The graph does not intersect with the y-axis.

Correct answer:

and

Explanation:

To find where the graph hits the y-axis, plug in 0 for x:

first evaluate 0 - 2 

then square -2

add 4 to both sides 

take the square root of both sides

now we have 2 potential solutions and need to solve for both

a)

b)

Example Question #9 : How To Find X Or Y Intercept

Which is neither an x- or y-intercept for the parabola

Possible Answers:

Correct answer:

Explanation:

The y-intercept(s) occur where the graph intersects with the y-axis. This is where x=0, so we can find these y-values by plugging in 0 for x in the equation:

The x-intercept(s) occur where the graph intersects with the x-axis. This is where y=0, so we can find these x-values by plugging in 0 for y in the equation:

add 16 to both sides

take the square root

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