Graphing & Using Intercepts

Graphing Using Intercepts

 

To find the 2 intercepts of a line (y and x) what you need to know is:

 

Any point on the y-axis has an x value of 0.

Any point on the x-axis has a y value of 0.

 

Knowing this you can find the intercept of any equation in slope intercept form.

 

Example

 

Y = -3x + 12

 

Finding the Y coordinate

 

Y = -3(0) + 12

Y = 12

 

The reason we replace x with 0 is because we are certain that any intercept point on the y-axis has a x value of 0/ therefore we replace x with 0 to solve for y.

 

 

Finding the X coordinate

 

0 = -3x + 12

0 - 12 = -3x + 12 – 12

-12/-3 = -3x/-3

4 = x

 

The reason we replace y with 0 is because we are certain that any intercept point on the x axis has a y value of 0 therefore we replace y with 0 to solve for x .

 

 

What do intercepts represent?

 

Every intercept represents something (mainly in application problems). Refer to the following example:

 

Example

 

The distance of a train is modeled by d = -50t + 200. Where d is distance in km and t is time in hours.

 

We know the d intercept is 200 because if you start at 0 and use the equation the answer will be 200.

 

To find the t intercept

 

D = -50t + 200

0 – 200 = -50t + 200 – 200

– 200/-50 = -50t/-50

4 = t

 

D intercept = (0,200)

Represents that initially the train Is 200km from the station

 

T intercept = (4,0)

Represents that after 4 hours of travel time the train reaches the station.

 

We know which are the y and x values because we know the original formula (y=mx+ b). Here the variables are just renamed.