In this section, you will review how to graph lines in slope-intercept form. Recall that slope-intercept form of a linear equation is an equation in which the constants m and b represent the slope and y-coordinate of the y-intercept, respectively.

slope-intercept form of a linear equation

Interactive exercise. Assistance may be required. Use the interactive below to investigate how to graph a line when the equation is in slope-intercept form. As you do, notice how the red points change. Also, notice how the vertical and horizontal distances change.

Graphing Lines in Slope-Intercept Form

Use the sliders to adjust the values of m and b for a line that is graphed in y = mx + b, or slope-intercept, form.

OnTRACK for College Readiness, Created with GeoGebra

Use the interactive to answer the questions below.

Pause and Reflect

The y-intercept of a line is sometimes called the starting point. When graphing a line whose equation is given in slope-intercept form, why do you think that is the case?

Interactive popup. Assistance may be required.

Check Your Answer

When you graph a line, you start by plotting the y-intercept using the value of b from the equation. Close Pop Up

Once you have the y-intercept plotted, how can you use the slope to obtain additional points?

Interactive popup. Assistance may be required.

Check Your Answer

The numerator of the slope tells you the change in vertical distance to the next point, and the denominator of the slope tells you the change in horizontal distance to the next point.Close Pop Up

Practice

Graph each of the following lines. Use an online graphing utility or graph paper and a pencil.

  1. y = 1 over 4 1 4 x + 3

    Interactive popup. Assistance may be required.

    Need a hint?

    Start with the y-intercept, and then use the slope to locate at least two more points. The numerator of the slope tells you how many vertical spaces to count, and the denominator of the slope tells you how many horizontal spaces to count.Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    Close Pop Up
  2. y = 0.6x − 4

    Interactive popup. Assistance may be required.

    Need a hint?

    Start with the y-intercept, and then use the slope to locate at least two more points. Rewrite the slope as a fraction. The numerator of the slope tells you how many vertical spaces to count, and the denominator of the slope tells you how many horizontal spaces to count.Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    Close Pop Up
  3. y = 5 over 3 5 3 x + 1

    Interactive popup. Assistance may be required.

    Need a hint?

    Start with the y-intercept, and then use the slope to locate at least two more points. The numerator of the slope tells you how many vertical spaces to count, and the denominator of the slope tells you how many horizontal spaces to count.Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    Close Pop Up