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:

- Find the slope using the slope formula
- \({\text{Slope}}={\text{m}}=\frac{\text{rise}}{\text{run}}=\frac{{\text{y}}_2-{\text{y}}_1}{{\text{x}}_2-{\text{x}}_1}\)
- \(\text{Point 1 or P}_{1}=(\text{x}_{1}, \text{y}_{1})\)
- \(\text{Point 2 or P}_{2}=(\text{x}_{2}, \text{y}_{2})\)

- 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.

- 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.

- Khan Academy: Slope-Intercept Equation from Two Points (06:41 mins, Transcript)
- Khan Academy: Slope-Intercept Form Problems (14:57 mins, Transcript)

Practice Problems

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

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