Download 8-05 Equation of a Line

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.
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
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
Example 1
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
4 = -6 + b
+6 +6
10 = b
substitute
simplify
y = 3x + 10
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
Example 2
Write an equation for the line containing the
points (1,5) and (2,8).
change in y-coordinates
m
change in x-coordinates
y2  y1
m
x2  x1
85
m
2 1
3
m 3
1
Example 2
Write an equation for the line containing the
points (1,5) and (2,8).
m3
y = mx + b
5 = 3(1) + b
5=3+b
-3 -3
2=b
y = 3x + 2
substitute
simplify
Practice 1
Write an equation for the line that contains the
given points.
1) (-4,1) (-1,4)
2) (-3,5) (-1,-3)
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).
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
+2
+2
y = -3x + 23
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
+4
+4
y = 7x - 17
Practice
Write an equation for the line with the given
point and slope.
1) (-3,0), m = -3
2) (4,3), m = ¾
Example 2
Write an equation for the line containing
(5,7) and (2,1).
y2  y1
First, find the slope: m 
17
6
m

2
25
3
x2  x1
y – y1 = m(x – x1)
y – 7 = 2(x – 5)
y – 7 = 2x - 10
+7
+7
y = 2x - 3
Practice
Write an equation for a line containing the
following points.
1) (12,16) (1,5)
2) (-3,5) (-1,-3)
Example 3
Write an equation for the line shown below.
First, find any two points on the line.
(-3,-3) and (1,-1)
2
1
m

4
2
y – y1 = m(x – x1)
y + 3 = ½(x + 3)
y + 3 = ½x + 1½
-3
-3
y = ½x – 1½
4
2
-4
-2
-2
-4
2
4