# GRE Math : How to find the equation of a curve

## Example Questions

### Example Question #112 : Coordinate Geometry

What is the slope of the line whose equation is ?

Explanation:

Solve for  so that the equation resembles the  form. This equation becomes . In this form, the  is the slope, which is .

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

Which of the following equations has a -intercept of ?

Explanation:

To find the -intercept, you need to find the value of the equation where .  The easiest way to do this is to substitute in  for your value of  and see where you get  for .  If you do this for each of your equations proposed as potential answers, you find that  is the answer.

Substitute in  for :

### Example Question #301 : Geometry

If  is a line that has a -intercept of  and an -intercept of , which of the following is the equation of a line that is perpendicular to ?

Explanation:

If  has a -intercept of , then it must pass through the point .

If its -intercept is , then it must through the point .

The slope of this line is .

Therefore, any line perpendicular to this line must have a slope equal to the negative reciprocal, which is . Only  has a slope of .

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