Intercepts and Slopes
This page introduces the concept of intercepts in linear equations and provides methods for finding them.
Definition: x-intercepts are the points on the graph that cross the x-axis y=0, while y-intercepts are the points on the graph that cross the y-axis x=0.
To find x-intercepts, set y = 0 in the equation and solve for x. The resulting point will be in the form x,0. For y-intercepts, set x = 0 and solve for y, resulting in a point of the form 0,y.
Example: For the equation 2x - 3y = 6, the x-intercept is found by setting y = 0:
2x - 30 = 6
2x = 6
x = 3
Therefore, the x-intercept is 3,0.
Similarly, the y-intercept is found by setting x = 0:
20 - 3y = 6
-3y = 6
y = -2
Thus, the y-intercept is 0,−2.
This method provides a systematic approach to finding intercepts, which is crucial for graphing linear equations and understanding their behavior.