Graphing with X- and Y-Intercepts

Learn to use x- and y-intercepts

to graph linear equations.

You can graph a linear equation easily by finding the x-intercept and the y-intercept. The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0).

Find the x-intercept and y-intercept of the line y = 4x + 4. Use the intercepts to graph the equation.

Find the x-intercept (?, 0).

y = 4x + 4

(0) = 4x + 4

-4 - 4-4 = 4x

The x-intercept is (-1, 0).

Find the y-intercept (0, ?).

y = 4x + 4

y = 4(0) + 4

y = 4

The y-intercept is (0, 4).

-1 = x

Plot both intercepts on the graph and draw in the line.

The graph of y = 4x + 4 is the line that crosses the x-axis at the point (-1, 0) and the y-axis at the point (0, 4).

Find the x-intercept and y-intercept of the line y = -3x - 6. Use the intercepts to graph the equation.

Find the y-intercept (0, ?).

Find the x-intercept (?, 0).

y = -3x - 6

(0) = -3x - 6

+6 _ +66 = -3x

The x-intercept is (-2, 0).

y = -3x - 6

y = -3(0) - 6

y = -6

The y-intercept is (0, -6).

-2 = x

Plot both intercepts on the graph and draw in the line.

The graph of y = -3x – 6 is the line that crosses the x-axis at the point (-2, 0) and the y-axis at the point (0, –6).

Find the x-intercept and y-intercept of the line y = 18 – 6x. Use the intercepts to graph the equation.

Find the x-intercept (?, 0).

y = 18 – 6x

(0)= 18 – 6x

0 = 18 – 6x

x = 3

The x-intercept is (3, 0).

Find the y-intercept (0, ?).

y = 18 – 6x

y = 18 – 6(0)

y = 18

The y-intercept is (0,18).

-18 -18-18 = – 6x

Plot both intercepts on the graph and draw in the line.

The graph of y = 18 – 6x is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, 18).