x-Intercepts and y-Intercepts

Definition

The x-intercept of a line is the point at which the line
crosses the x axis. ( i.e. where the y value equals 0 )

x-intercept = ( x, 0 )

The y-intercept of a line is the point at which the line
crosses the y axis. ( i.e. where the x value equals 0 )

y-intercept = ( 0, y )

 

Example Problem

Find the x and y intercepts of the equation 3x + 4y = 12.

Solution

To find the x-intercept, set y = 0 and solve for x.

 

 3x + 4( 0 ) = 12
 3x + 0 = 12
 3x = 12
 x = 12/3
 x = 4

 

To find the y-intercept, set x = 0 and solve for y.

 

 3( 0 ) + 4y = 12
 0 + 4y = 12
 4y = 12
 y = 12/4
 y = 3

 

Therefore, the x-intercept is ( 4, 0 ) and the y-intercept
is ( 0, 3 ).

The graph of the line looks like this:

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