1. 6 minutes
Warm-Up
1. Find the slope of the line containing the points (-2,5) and (4,6).
2. Find the slope of the line y = x – 9.
3. Find the slope of the line 3y – 4x = 9.

2. Equation of a Line Objectives:
To write an equation of a line using the slope-intercept equation
To write an equation of a line using the point-slope equation

3. The Slope-Intercept Equation
y = mx + b
slope
y-intercept
Create an equation of a line with a slope of -3 and a y-intercept of 4.
y = -3x + 4
y = 4 – 3x
3x = 4 - y
-4 = -y – 3x

4. Example 1 y = mx + b 4 = 3 (-2) + b 4 = -6 + b +6 +6 10 = b
Write an equation for the line with slope 3 that contains the point (-2,4)
y = mx + b
solve for b 4 = 3
(-2)
+ b
substitute
simplify
4 = -6 + b +6 +6
10 = b
y = 3x + 10

5. Practice
Write an equation for the given line that contains the given point and has the given slope.
1) (5,10); m = 4
2) (-3,8); m = 2

6. Example 2
Write an equation for the line containing the points (1,5) and (2,8).

7. Example 2 y = mx + b 5 = 3 (1) + b 5 = 3 + b -3 -3 2 = b y = 3x + 2
Write an equation for the line containing the points (1,5) and (2,8).
y = mx + b
substitute 5 = 3
(1)
+ b
simplify
5 = 3 + b -3 -3
2 = b
y = 3x + 2

8. Practice 1
Write an equation for the line that contains the given points.
1) (-4,1) (-1,4)
2) (-3,5) (-1,-3)

9. Practice 2
1. Write an equation for the line with slope -2 and containing the point (-3,0).
2. Write an equation for the line containing the points (0,0) and (4,2).

10. The Point-Slope Equation
y – y1 = m(x – x1)
Create an equation of a line with a slope of -3 that contains the point (7,2).
y – 2 = -3(x – 7)
y – 2 = -3x + 21
y = -3x + 23

11. Example 1
Write an equation for the line with slope 7 that contains the point (3,4).
y – y1 = m(x – x1)
y – 4 = 7(x – 3)
y – 4 = 7x - 21
y = 7x - 17

12. Practice
Write an equation for the line with the given point and slope.
1) (-3,0), m = -3
2) (4,3), m = ¾

13. Example 2
Write an equation for the line containing (5,7) and (2,1).
First, find the slope:
y – y1 = m(x – x1)
y – 7 = 2(x – 5)
y – 7 = 2x - 10
y = 2x - 3

14. Practice Write an equation for a line containing the following points.
1) (12,16) (1,5)
2) (-3,5) (-1,-3)

15. Example 3
Write an equation for the line shown below.
First, find any two points on the line.
(-3,-3)
and
(1,-1) 4 2 -4 -2 2 4
y – y1 = m(x – x1) -2 -4
y + 3 = ½(x + 3)
y + 3 = ½x + 1½
y = ½x – 1½