Slope-Intercept:

How to Find the Equation of a Line from Two Points

The following video will teach how to find the equation of a line, given any two points on that line.

Video Source (7:13 mins) | Transcript

Steps to find the equation of a line from two points:

  1. Find the slope using the slope formula
    • \({\text{Slope}}={\text{m}}=\frac{\text{rise}}{\text{run}}=\frac{{\text{y}}_2-{\text{y}}_1}{{\text{x}}_2-{\text{x}}_1}\)
    • \(\text{Point 1 or P}_{1}=(\text{x}_{1}, \text{y}_{1})\)
    • \(\text{Point 2 or P}_{2}=(\text{x}_{2}, \text{y}_{2})\)
  2. Use the slope and one of the points to solve for the y-intercept (b).
    • One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
  3. Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Additional Resources

Practice Problems

For each of the following problems, find the equation of the line that passes through the following two points:

  1. \(\left ( -5,10 \right )\) and \(\left ( -3,4 \right )\)
  2. \(\left ( -5,-26 \right )\) and \(\left ( -2,-8 \right )\)
  3. \(\left ( -4,-22 \right )\) and \(\left ( -6,-34 \right )\)
  4. \(\left ( 3,1 \right )\) and \(\left ( -6,-2 \right )\)
  5. \(\left ( 4,-6 \right )\) and \(\left ( 6,3 \right )\)
  6. \(\left ( 5,5 \right )\) and \(\left ( 3,2 \right )\)

Solutions

  1. \({\text{y}}=-3{\text{x}}-5\) (Written Solution)

  2. \({\text{y}}=6{\text{x}}+4\)

  3. \({\text{y}}=6{\text{x}}+2\) (Written Solution)

  4. \({\text{y}}=\frac{1}{3}{\text{x}}\)

  5. \({\text{y}}=\frac{9}{2}{\text{x}}-24\)

  6. \(\text{y}=\frac{3}{2}{\text{x}}{-}{\frac{5}{2}}\)