Convert from Standard Form to Slope-Intercept Form

Standard Form to Slope-Intercept Form

​Vocabulary Review

Variable Terms: Terms in an expression or equation that contain a variable.

Coefficient: The number in a variable terms that is "next to" the variable.

Constant: Terms in an expression or equation that do not contain a variable.

​Example: 2x - 3y = 10
2x and -3y are variable terms.
2 is the coefficient of the x-term.
-3 is the coefficient of the y-term.
10 is a constant.

Multiple Choice

What is the coefficient of the x-term?

$$y+8=-5x$$

• -5

• 8

• 5

• 1

Multiple Choice

Identify the constant:

$$y-9=4x$$

• 1

• -9

• 9

• 4

Multiple Choice

Identify the coefficient of the y-term.

$$3x+y=-18$$

• -18

• 3

• 18

• 1

Multiple Choice

Identify the coefficient of the y-term

$$-y=10x-3$$

• -1

• 1

• -3

• 3

Multiple Choice

Slope-Intercept Form: $$y=mx+b$$

Which equation is written in slope-intercept form?

• $$x=2y+10$$

• $$5x-3y=10$$

• $$2y=\frac{9}{5}x+7$$

• $$y=\frac{5}{6}x-1$$

Complete these problems along with the slides that follow.

​Complete these problems along with the slides that follow.

Copy all steps onto your handout for both examples & read the following explanation.​

1st Problem: To "move" -9 away from y, add 9 to both sides.
3x and 9 cannot be combined, write 3x and 9 as an expression.
y = 3x + 9 is the new equation
2nd Problem: To "move 2x away from y, subtract 2x from both sides.
-4 and -2x cannot be combined, write -4 and -2x combined as an expression.
y = -4 - 2x can also be written as y = -2x - 4.

Poll

You will now complete the "Type 1" problems on side 1 of your handout along with the following slides.

Notice that all of the "Type 1" problems contain a y term that has a coefficient of 1, so there is no number in front of y.

Show all of the steps necessary to complete each problem.

Read all of the information that is provided on each slide.

• I will read all of the information provided on each slide and show all steps necessary to complete each problem.

• I will read all of the information provided on each slide and show all steps necessary to complete each problem.

Multiple Choice

#1 $$y+3x=9$$

Explain how to isolate y.

• Subtract 3x

• Add 3x

• Subtract 9

• Add 9

Multiple Choice

#1 $$y+3x=9$$

Subtract 3x from both sides on your handout to isolate y.

What is the new equation?

• $$y=-3x+9$$

• $$y=3x+9$$

Multiple Choice

#2 $$x+y=-3$$

Explain how to isolate y.

• Add x

• Subtract x

• Subtract y

• Add 3

Multiple Choice

#2 $$x+y=-3$$

Subtract x from both sides on your handout to isolate y.

What is the new equation?

• $$y=x-3$$

• $$y=-x-3$$

Multiple Choice

#3 $$15+y=2x$$

Explain how to isolate y.

• Add 2x

• Subtract 2x

• Subtract 15

• Add 15

Multiple Choice

#3 $$15+y=2x$$

Subtract 15 from both sides on your handout to isolate y.

What is the new equation?

• $$y=2x-15$$

• $$y=2x+15$$

Poll

You will now complete the "Type 2" problems on side 2 of your handout along with the following slides.

Notice that all of the "Type 2" problems contain a y-term with a coefficient of -1, so there is only a negative sign in front of the y.

Show all of the steps necessary to complete each problem.

Read all of the information that is provided on each slide.

• I will read all of the information provided on each slide and show all steps necessary to complete each problem.

• I will read all of the information provided on each slide and show all steps necessary to complete each problem.

​1st Problem
Step 1: To "move" -8 away from -y, add 8 to both sides.
x and 8 cannot be combined, write x and 8 as an expression.
-y = x + 8 is the new equation
Step 2: Divide all terms be -1 and simplify.
The simplified equation is y=-x-8.

​Copy all steps onto your handout for both examples & read the following explanations.

​2nd Problem
Step 1: To move 10x away from -y, subtract 10x from both sides.
-1 and -10x cannot be combined, write -1 and -10x combined as an expression.
-y=-10x-1 is the new equation.
Step 2: Divide all terms by -1 and simplify.
The simplified equation is y=10x+1

Multiple Choice

#4 $$7x-y=8$$

Explain the first step to isolate y.

• Subtract 7x

• Add 7x

Multiple Choice

#4

Subtract 7x from both sides of the equation.

$$-y=-7x+8$$

What is the next step to isolate y?

• Divide all terms by -1

• Add 1 to all terms

Multiple Choice

#4

$$-y=-7x+8$$

Divide all terms by -1 and simplify.

• $$y=7x-8$$

• $$y=7x+8$$

• $$y=-7x-8$$

Multiple Choice

#5 $$4-y=-x$$

Explain the first step to isolate y.

• Add 4

• Subtract 4

• Add x

Multiple Choice

#5 Subtract 4 from both sides.

$$-y=-x-4$$

What is the next step to isolate y?

• Divide all terms by -1

• Add y to both sides

Multiple Choice

#5 Divide all terms by -1 and simplify.

• $$y=x-4$$

• $$y=x+4$$

Multiple Choice

#6 $$-y=6x$$

Explain how to isolate y.

• Divide by 6

• Divide by -1

• Subtract 6x

Multiple Choice

#6 Divide by -1

• $$y=6x-1$$

• $$y=6x$$

• $$y=-6x$$

Poll

You will now complete the "Type 3" problems on side 2 of your handout along with the following slides.

Notice that all of the "Type 3" problems contain a y-term with a coefficient other than 1 or -1, so there is a number in front of the y.

Show all of the steps necessary to complete each problem.

Read all of the information that is provided on each slide.

• I will read all of the information provided on each slide and show all steps necessary to complete each problem.

• I will read all of the information provided on each slide and show all steps necessary to complete each problem.

​1st Problem
Step 1: To "move" 4x away from 2y, subtract 4x from both sides.
-8 and -4x cannot be combined, write -8 and -4x as an expression.
2y = -4x - 8 is the new equation
Step 2: Divide all terms be 2 and simplify.
The simplified equation is y=-2x-4.

​2nd Problem
Step 1: To move 6 away from -2y, subtract 6 from both sides.
x and -6 cannot be combined, write x and -6 combined as an expression.
-2y=x-6 is the new equation.
Step 2: Divide all terms by -2 and simplify.
The simplified equation is y=-1/2x+3

​Copy all steps onto your handout for both examples & read the following explanations.

Multiple Choice

#7 $$8x-4y=12$$

Explain the first step to isolate y.

• Subtract 8x

• Divide by -4

• Add 8x

Multiple Choice

#7 Subtract 8x from both sides to get:

$$-4y=-8x+12$$

What is the next step to isolate y?

• Add 4y

• Divide by -4

Multiple Choice

#7 Divide all terms by -4 to get:

• $$y=2x-3$$

• $$y=-2x+3$$

Multiple Choice

#8 $$16+4y=-6x$$

Explain the first step to isolate y.

• Add 6x

• Divide by 4

• Subtract 16

Multiple Choice

#8 Subtract 16 from both sides to get

$$4y=-6x-16$$

What is the next step to isolate y?

• Divide all terms by -4

• Divide all terms by 4

Multiple Choice

#8 Divide all terms by 4 and simplify to get:

• $$y=\frac{6}{4}x-4$$

• $$y=-\frac{3}{2}x-4$$

Multiple Choice

#9 $$-x+3y=9$$

Add x to both sides to get 3y=x+9 and then divide all terms by 3 to get:

• $$y=\frac{1}{3}x+3$$

• $$y=3x+3$$