How can you tell a number is the x intercept in an equation?

Question

I need to know how I can find out if a number is the x intercept without a graph. Also the y intercept

Answer 1

helped me to think of intercepts as points.  (X,Y)

(X,0) y=0 gives the X-intercept, value of x

(0,Y) x=0 give the Y-Intercept, value of y

Answer 2

Hello, Jahrealle --

To find the x-intercept, set y equal to 0, and solve for x. To find the y-intercept, let x equal 0.

Here is an example:

     2x + 3y  =  6

to find the x-intercept, we will substitute 0 for y:

     2x + 3(0) = 6
      2x +    0  = 6
          x = 3
The x-intercept is the point (3,0)

To find the y-intercept, substitute 0 for x:

     2(0) + 3y  =  6
         0  + 3y =  6
                  y  =  2

The y-intercept is the point (0,2).

You did not ask how to find the slope, but here it would be (2-0)/(0-3), or -2/3

Answer 3

Plug it into your equation and determine the value of y. If you get y = 0, then the value of x is an x-intercept. Otherwise it's not an x-intercept

For example, let y = 3x - 6.

Then 2 is an x-intercept since if x = 2 then y = 3*2 - 6 = 6 - 6 = 0,

while 3 is not an x-intercept since if x = 3 then y = 3*3 - 6 = 9 - 6 = 3 ≠ 0.

 

The similar thing applies to y-intercept, but this time you need to check if x = 0.

Most of your equations will be those that express y in terms of x, like the equation above. In that case you can find the y-intercept by plugging in x = 0. In the example above, the y-intrcept is -6.