Download Finding x and y Intercepts and more Slides Pre-Calculus in PDF only on Docsity!
Finding x and y Intercepts
The x -intercept is the point at which a graph crosses the x -axis. As the y value is zero anywhere along the x -axis, the x -intercept is an ordered pair of numbers where the y value is always zero. The points (โ3, 0), (1, 0), (4, 0) are all examples of points on the x -axis.
x
y
The y -intercept is the point at which a graph crosses the y -axis. As the x value is zero anywhere along the y -axis, the y -intercept is an ordered pair of numbers where the x value is always zero. The points (0, 1), (0, โ1), and (0, 2) are all examples of points on the y -axis.
x
y
It is possible to graph the equation of a line by finding the x - and y -intercepts.
EXAMPLE: We will graph the equation 3 x + 2 y = 12 by finding the x - and y -intercepts.
- Graph the ordered pairs and draw the line.
- To find the x -intercept, let y = 0 and solve for x.
3 2 1 3 2(0) 1 3 1 4
x y x x x
- To find the y -intercept, let x = 0 and solve for y. 3 2 12 3(0) 2 12 2 1 6
x y y y y
The y -intercept is the ordered pair (0, 6).
The x -intercept is the ordered pair (4, 0).
x
y (0, 6)
EXAMPLE: Find the x - and y -intercepts of y = 2 x + 6 and graph.
x
y (0, 6)
- Find the y -intercept. ( x will be 0) 2 6 2(0) 6 6
y x y y
The y -intercept is (0, 6).
- Graph the intercepts and draw the line.
- Find the x -intercept. ( y will be 0)
2 6 0 2 6 6 2 3
y x x x x
The x -intercept is (โ3, 0).
EXERCISES: Find the x - and y -intercepts of the following equations and graph the line of each equation.
a. y = 2 x + 8 b. y = 5 x + 10 c. x โ 3 y = 6 d. 3 x โ 4 y = 12 e. 2 x โ 4 y = 8 f. 2 x + 3 y = 0
KEY: a. (^) x -intercept: (โ4, 0) y -intercept: (0, 8)
x
y (0, 8)
(โ 4 , 0)
b. (^) x -intercept: (โ2, 0) y -intercept: (0, 10)
x
y
(0, 10)
(โ 2 , 0)
c. x -intercept: (6, 0) y -intercept: (0, โ2)
x
y
d. x -intercept: (4, 0) y -intercept: (0, โ3)
x
y
e. x -intercept: (4, 0) y -intercept: (0, โ2)
x
y
f. x -intercept: (0, 0) You will need another point y -intercept: (0, 0) to complete the graph.
x
y
