High School Math : Intercepts and Curves

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #21 : How To Find X Or Y Intercept

What is the y-intercept of the following line: 

 ? 

Possible Answers:

Correct answer:

Explanation:

The y-intercept is precisely the point in which the x-value is . Thus, we plug in  to our equation and solve for 

Thus our intercept is 

Example Question #22 : How To Find X Or Y Intercept

What is the -intercept of the equation?

Possible Answers:

Correct answer:

Explanation:

To find the x-intercept of an equation, set the  value equal to zero and solve for .

Subtract  from both sides.

Divide both sides by .

Since the x-intercept is a point, we will write our answer in point notation: .

Example Question #23 : How To Find X Or Y Intercept

Find the -intercept of

Possible Answers:

Correct answer:

Explanation:

Put the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

-5y = 3x + 10

y = (-3/5)x + 10/(-5)

 

Now we can easily see that is the -intercept. 

Example Question #24 : How To Find X Or Y Intercept

A straight line passes through the points  and .

What is the -intercept of this line?

Possible Answers:

Correct answer:

Explanation:

First calculate the slope:

The standard equation for a line is  .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get .

Therefore, .

Our equation for the line is now:

To find the -intercept, we plug in :

 

 

Thus, the -intercept the point (4,0).

Example Question #25 : How To Find X Or Y Intercept

Calculate the y-intercept of the line depicted by the equation below.

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept, let  equal 0.

We can then solve for the value of .

The y-intercept will be .

Example Question #26 : How To Find X Or Y Intercept

What is the x-intercept of ?

Possible Answers:

Correct answer:

Explanation:

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

Subtract  from both sides:

Divide both sides by  to isolate x:

Example Question #21 : Intercepts And Curves

What is the y-intercept of the equation?

Possible Answers:

Correct answer:

Explanation:

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

Since the y-intercept is a point, we will need to convert our answer to point notation.

Example Question #1 : How To Find The Equation Of A Curve

What line goes through points and ?

Possible Answers:

Correct answer:

Explanation:

First, we find the slope between the two points:

and

Plug the slope and one point into the slope-intercept form to calculate the intercept:

 

 

Thus the equation between the points becomes .

Example Question #1 : How To Find The Equation Of A Circle

The center of a circle is  and its radius is . Which of the following could be the equation of the circle? 

Possible Answers:

Correct answer:

Explanation:

The general equation of a circle is , where the center of the circle is  and the radius is .

Thus, we plug the values given into the above equation to get 

Example Question #2 : How To Find The Equation Of A Circle

Which one of these equations accurately describes a circle with a center of and a radius of ?

Possible Answers:

Correct answer:

Explanation:

The standard formula for a circle is , with the center of the circle and the radius.

Plug in our given information.

This describes what we are looking for.  This equation is not one of the answer choices, however, so subtract from both sides.

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