1. “I can write an equation of a line, given two points on the line.”
Writing Equations
“I can write an equation of a line, given two points on the line.”

2. What do we already know? An equation for a line has the form: .
We need to know the to write the equation for the line.
We also need the intercept to complete the equation for a line.

3. The Slope Formula
If we know nothing else about the line, we can find its equation given two points on the line.
We’ll use the slope formula.

4. Using the slope formula
Example 1:
Find the slope of the line through the points (-2, 4) and (5, -3).

5. Using the slope formula
Practice:
Given the points, find the slope:
(1, -19) and (-2, -7)
(9, 3) and (19, -17)

6. Finding the y-intercept
Once we have the slope, we need to complete the equation by finding the y-intercept (b).
y = mx + b
From the previous practice problem, with points (9, 3) and (19, -17). We found the slope (m) was -2.
Any ideas on how we can now find b?

7. Finding the y-intercept
For our problem, we have two points (9, 3) and (19, -17) and slope of -2.
We need to use one of these points and the slope to solve for b.
y = mx + b
y = -2x + b (using slope we already found)
3 = -2(9) + b (substitute in x and y from our points)

8. Finding the y-intercept
For our problem, we have two points (9, 3) and (19, -17) and slope of -2.
We need to use one of these points and the slope to solve for b.
y = mx + b
y = -2x + b (using slope we already found)
3 = -2(9) + b (substitute in x and y from our points)
21 = b (solve for b)
y = -2x Put it all together!

9. Another Example
Find the equation for the line that goes through the point: (2, -7) and (4, 5)
Step 1: Find the Slope
Step 2: Put the Slope into the equation
Step 3: Substitute (x,y) into the equation
Step 4: Solve for b
Step 5: Put it all together

10. Practice
Find the equation for the lines that go through the following points:
(6, -12) and (15, -3)
(4, 3) and (2, 1)

11. Closure
In your own words, describe the steps to find the equation of a line given two points on the line.