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.

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.

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. $$\text{y}=\frac{3}{2}{\text{x}}{-}{\frac{5}{2}}$$