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

How to Find the Equation of a Line From Two Points

Video Source (7:13 mins) | Transcript

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

- Find the slope using the slope formula.
- \( Slope = m = {\dfrac {rise}{run}} = {\dfrac {y2−y1} {x2−x1}} \)
- Point 1 or \( P1= (x1,y1) \)
- Point 2 or \( P2= (x2,y2) \)

- 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.

## Additional Resources

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

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