Writing the Equation of a Line in Slope-Intercept Form From a Graph

The y-intercept b and the slope m of a line must be found to write the equation of the graph of the line in slope-intercept form . y=mx+b Consider the line shown as an example.

There are four steps to writing the equation of this line.

Find the y-Intercept

The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This line intercepts the y-axis at (0,- 4), which means that the y-intercept is - 4.

Replace b With the y-Intercept

The y-intercept can be substituted into the slope-intercept form equation for b. y=mx+ b ⇓ y=mx - 4

Find the Slope

Next, the slope of the line must be determined. The slope of a line is the ratio of the rise and run of the line. m=rise/run The rise is the vertical distance between two points and the run is the horizontal distance. Any two points on the line can be used to find the slope.

For this line, the rise is 6 and the run is 2. Substitute these values into the formula to calculate the slope of the line. m=6/2 ⇒ m=3

Replace m With the Slope

Finally, substitute m= 3 in to the equation from Step 2 to complete the equation. y= mx-4 ⇓ y= 3x-4 The equation of the line in slope-intercept form is now complete.

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