1. -3 -3x -3x -3 -3 -3 3:7 Standard Form
Lesson 3.7 Standard Form
3:7 Standard Form
Objective- To graph and manipulate equations in standard form.
Slope-Intercept Form
Standard Form
y = mx + b
Ax + By = C -3
3x + 2y = 8
y = x + 4
-3x x 2
2y = -3x + 8 -3
m = 2 -3 8
b = 4
y = x + 2 2
To change Standard Form to Slope-Intercept Form
just solve the equation for y. -3
y = x + 4 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. -4x + 3y = 6 Graph the following equation. +4x +4x y +3 3y = 4x + 6 +4 4 6
y = x + 3 3 4
y = x + 2 3 x 4
m = 3
b = 2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. -2x -2x -2 -1 -1 -1 Graph the following equation. 2x + 6y = 3 y
6y = -2x + 3 -2 3
y = x + 6 6 -1 1
y = x + 3 2 -1 x -1 +3
m = 3 1
b = 2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. Graph the following equation.
y = x y
y = 1x + 0
m = 1
b = 0 +1 +1 x
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. Convert the following linear equation to standard form.
y = 2x + 5
Not in standard form!
-2x -2x
Ax + By = C
-2x + y = 5
-2x + y = 5 or
2x - y = -5
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. Convert the following linear equation to standard form.
Not in standard form!
Ax + By = C
Where A, B and C
are integers.
-x + 2y = -2 or
x - 2y = 2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7. Convert the following linear equation to standard form.
Not in standard form!
Ax + By = C
Where A, B and C
are integers.
2x + 3y = 21
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. Convert the following linear equation to standard form.
Not in standard form!
Where A, B and C
are integers.
3y = 5x - 12
Ax + By = C
-5x -5x
-5x + 3y = -12 or
5x - 3y = 12
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

9. Convert the following linear equation to standard form.
Not in standard form!
Where A, B and C
are integers.
5y = -3x - 40
Ax + By = C
+3x +3x
3x + 5y = -40
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

10. No fractional coefficients!
Write a linear equation in standard form given: 2
slope = y-intercept = 4 3
y = mx + b 2
y = x + 4
Not in standard form! 3
Ax + By = C 2 2
- x x 3 3
Where A, B and C
are integers. 2
x + y = 4 3 2 3
x + y = 4
No fractional coefficients! 3
- 2x + 3y = 12
2x - 3y = -12 or
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

11. No fractional coefficients!
Write a linear equation in standard form given: 5
slope = y-intercept = -1 4
y = mx + b 5
y = x - 1
Not in standard form! 4
Ax + By = C 5 5
- x x 4 4
Where A, B and C
are integers. 5
x + y = -1 4 5 4
- x + y = -1
No fractional coefficients! 4
- 5x + 4y = -4
5x - 4y = 4 or
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

12. Let p = # of pens purchased Let r = # of rulers purchased 3p + 1r = 12
Pens cost $3 each and rulers cost $1 each. If Jim spends $12, how many of each did he buy?
Let p = # of pens purchased
Let r = # of rulers purchased
3p + 1r = 12 12 10 8 6 4 2
-3p p
1r = -3p +12
# Rulers
r = -3p +12
m = -3
b = 12
# Pens
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series