Lines and the Coordinate Plane: Graphing the Equation of a Line

Slope-Intercept Form

Sometimes, you have two points, but no graph.  You can still find the equation of the line in slope-intercept form.

Step 1: Find the slope of the line.
Step 2: Plug the slope of the line and either of the points into the general equation.
Step 3: Solve the equation for b.
Step 4: Write the equation.


Example 1 

Determine the equation of the line between (1, 3) and (4, 6) in slope-intercept form.

Step 1:  Find the slope of the line.

y 2 minus y 1 divided by x 2 minus x 1 equals 6 minus 3 divided by 4 minus 1 equals 3 divided by 3 equals 1, m equals 1

Step 2: Plug the slope of the line and either of the points into the general equation.

y = mx + b

6 = 1(4) + b

Step 3: Solve the equation for b.

6 = 1(4) + b

6 = 4 + b

2 = b

Step 4:  Write the equation.

We now know that m = 1 and b =2.  Plug these values into the general equation.

y = mx + b

y = 1x + 2

So, y = 1x + 2 is the equation of the line between (1, 3) and (4, 6)