Write Slope-Intercept Form From a Graph

Goal

Write the equation of a line in slope-intercept form:

[ y = mx + b ]

Here, m is the slope and b is the y-intercept.

Method

1. Find the y-intercept

   • Look for the point where the line crosses the y-axis.
   • That value is b.

2. Find the slope

   • Pick two clear points on the line.
   • Use the slope formula: [ m = \frac{y_2 - y_1}{x_2 - x_1} ]
   • Simplify the fraction if possible.

3. Write the equation

   • Substitute the slope for m and the y-intercept for b.
   • Your answer should look like: [ y = mx + b ]

Check your work

• Does the line cross the y-axis at the correct value?
• If you move along the line, does the rise over run match your slope?
• If possible, test another point from the graph in your equation.

Tips

• If the line goes up as you move right, the slope is positive.
• If it goes down as you move right, the slope is negative.
• Horizontal lines have slope 0, so the equation is (y = b).