Algebra 1 Notes SOL A.6 (4.3) Graphing Using Intercepts Mrs. Grieser
1
Name: _______________________________ Block: _______ Date: _____________
Intercepts
An x-intercept is a point where a function crosses the x-axis.
The y-intercept is the point where a function crosses the y-axis.
A line is a geometric figure determined by two points. When graphing a
linear equation, we therefore only need two points. Two relatively easy
points to find are the x- and y-intercepts.
Recall that the ordinate (y-value) of all points on the x-axis is 0, and that
the abscissa (x-value) of all points on the y-axis is 0. Therefore, if we
want to find the points where a linear function crosses the x-axis (the x-intercept), we would
set the output value (the y-value) to 0 and solve for x, and to find where it crosses the y-axis
(the y-intercept), we would set the input value (the x-value) to 0 and solve for y.
Example: Find the x- and y-intercepts of 2x + 7y = 28.
Find the x-intercept:
Set y = 0, because the ordinate of the point on the x-axis is 0. Then solve for x.
2x + 7(0) = 28
2x = 28
x = 14
The x-intercept is (14, 0).
Find the y-intercept
:
Set x = 0, because the abscissa of the point on the y-axis is 0. Then solve for y.
2(0) + 7x = 28
7x = 28
x = 4
The y-intercept is (0, 4).
You try: find the x- and y-intercepts for the following linear equations:
1) 3x + 2y = 6
2) 4x
–
2y = 10
3)
-
3x + 5y =
-
15
**
Remember: set
y = 0 to find the x
-
intercept, and x = 0 to find the y
-
intercept.
