1. Lesson 3.8 Writing Linear Equations Given Two Points
Objective- To write a linear equation given a point
and a slope or given two points.
Write a linear equation in standard form given:
slope = y-intercept = -2
m = b = -2
y = mx + b
y = 3x + -2
Not in standard form!
-3x -3x
Ax + By = C
-3x + y = -2
Where A, B and C
are integers. or
3x - y = 2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

2. No fractional coefficients!
Write a linear equation in standard form given: 1
slope = y-intercept = -2 4
y = mx + b 1
y = x - 2
Not in standard form! 4
Ax + By = C 1 1
- x x 4 4
Where A, B and C
are integers. 1
x + y = -2 4 1 4
- x + y = -2
No fractional coefficients! 4
- x + 4y = -8
x - 4y = 8 or
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. -1 (x,y) y = mx + b -1 -1 y = x + y = x + b -1 4 = (2) + b -2 4 = + b
Write a linear equation in standard form given: -1
slope = point = (2,4) 5
(x,y)
y = mx + b -1 22 -1
y = x +
y = x + b 5 5 5 1 1 -1
+ x x
4 = (2) + b 5 5 5 -2
4 = b 1 22 5
x + y = 5 5 5 2 2 5 5
x + 5y = 22 2 22
= b = 5 5
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. -11 -2 = (1) + b -2 = + b -11 -14 -11 -3 (x,y) y = mx + b -3 -3
Write a linear equation in standard form given: -3
slope = point = (1,-2) 7
(x,y)
y = mx + b -3
-11 -3
y = x +
y = x + b 7 7 7 3 3 -3
+ x x
-2 = (1) + b 7 7 7 -3
-2 = b
-11 3 7
x + y = 7 7 7 3 3 7 7
3x + 7y = -11 3
= b 7
-14
-11 3
= b = 7 7 7
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. -12 - x - x -3 -12 - - -3x + 5y = -12 -12 -12 (x,y) y = mx + b (4,0)
Write a linear equation in standard form given: 3
slope = x-intercept = 4 5
(x,y)
y = mx + b
(4,0)
-12 3
y = x + 3
y = x + b 5 5 5
- x x 3 3 3
0 = (4) + b 5 5 5 12 -3
-12
0 = b 5
x + y = 5 5 5 12 12 5 5
-3x + 5y = -12
-12
-12
= b = or 5 5
3x - 5y = 12
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. Change in price = $0.80/ brick y = 0.80x + b m = 0.80
A masonry company charges $0.80 a brick. The
company will charge $465 for 500 bricks to be
delivered to a site. If x = the number of bricks, and
y = total cost, write an equation for y in terms of x.
Slope
y = mx + b
Change in price = $0.80/ brick
y = 0.80x + b
m = 0.80
465 = 0.8(500) + b
465 = b
Point
500 bricks cost $465
65 = b
(x, y) = (500, 465)
y = 0.8x + 65
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7. Finding an Equation Given Two Points
y = mx + b 1
Write the equation of
the line which contains:
y = x + b 3 1
5 = (4) + b
(-2, 3) (4, 5) 3
(x, y) 4
y2- y1
5 = b y 3
Slope (m) = = x
x2- x1 4 15 4
b = 5 - - =
5 - 3 3 3 3 2
Slope (m) = =
4 - -2 11 6
b = 1 11 1 3
y = x +
m = 3 3 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. the line which contains:
Write the equation of
the line which contains:
(0, -3) (4, 8)
y = mx + b
(x, y) 11
y = x + b
y2- y1 4 y
Slope (m) = = x
x2- x1 11
8 = (4) + b 4
8 - -3 11
Slope (m) = =
4 - 0
8 = b 4 11
b =
= -3
m = 4
b = -3 11
y = x - 3 4
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

9. -3.95 -3.95 Suppose a 5 minute call costs $6.20 and a
20 minute call costs $ Write an equation
which describes cost y in terms of x minutes.
(minutes, cost)
(x, y)
(5, 6.20) (20, 18.05)
y = mx + b
y2- y1
y = 0.79x + b
m = =
x2- x1
20 - 5
6.20 = 0.79(5) + b
11.85
m = =
0.79
6.20 = b 15
2.25 = b
y = 0.79x
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

10. -12 -12 Use the x-y chart below to write a linear
equation that satisfies all the points. x y
y = mx + b +2 +6
y = 3x + b +3 +9
10 = 3(4) + b +2 +6 +5
+15
10 = 12 + b
y2- y1
10 - 4
-2 = b
m = =
x2- x1
4 - 2 6
m = = 3
y = 3x - 2 2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series