Representations of Linear Functions

1. y = 5x + 10

Slope: ___

Y-intercept: ___

• Slope: 10

  Y-intercept: 5

• Slope: 5

  Y-intercept: 10

• Slope: -5

  Y-intercept: 10

• Slope: 5

  Y-intercept: -10

Answer explanation

The # being multiplied by the variable is the slope, so we locate 5x and identify the slope = 5. The # being added/subtracted once is the y-intercept, so y-intercept = 10.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

2. y = 3x - 200

Slope: ___

Y-intercept: ___

• Slope: 3

  Y-intercept: 200

• Slope: 200

  Y-intercept: 3

• Slope: 3

  Y-intercept: -200

• Slope: -200

  Y-intercept: 3

Answer explanation

The # being multiplied by the variable is the slope, so we locate 3x and identify the slope = 3. The # being added/subtracted once is the y-intercept, so y-intercept = -200.

Also, remember to look IN FRONT of the number for its sign.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

3. y = -2x - 1

Slope: ___

Y-intercept: ___

• Slope: -1

  Y-intercept: -2

• Slope: -2

  Y-intercept: -1

• Slope: 2

  Y-intercept: 1

• Slope: 2

  Y-intercept: -1

Answer explanation

The # being multiplied by the variable is the slope, so we locate -2x and identify the slope = -2. The # being added/subtracted once is the y-intercept, so y-intercept = -1.

Also, remember to look IN FRONT of the number for its sign.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

4. y = 5 - 7x

Slope: ___

Y-intercept: ___

• Slope: -7

  Y-intercept: 5

• Slope: 5

  Y-intercept: -7

• Slope: 7

  Y-intercept: 5

• Slope: -5

  Y-intercept: 7

Answer explanation

The # being multiplied by the variable is the slope, so we locate -7x and identify the slope = -7. The # being added/subtracted once is the y-intercept, so y-intercept = 5.

**CAREFUL because the numbers are not always in the same order.

Also, remember to look IN FRONT of the number for its sign.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

5. y = x

Slope: ___

Y-intercept: ___

• Slope: 0

  Y-intercept: 1

• Slope: 0

  Y-intercept: 0

• Slope: 1

  Y-intercept: 1

• Slope: 1

  Y-intercept: 0

Answer explanation

The # being multiplied by the variable is the slope, so we locate x and identify the slope = 1 since there is an INVISIBLE 1 in front of any lonely variable. We usually don't write 1x because that is silly and it is obvious there is one x.

The # being added/subtracted once is the y-intercept, so y-intercept = 0 since nothing is being added or subtracted.

Tags

CCSS.8.EE.B.5

Describe how you knew how to identify the slope versus the y-intercept in all of the equations #s 1-5.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

• Y-intercept: +3

• Y-intercept: -3

• Y-intercept: 1

Answer explanation

We locate x=0 on the table and see that y=1, so the y-intercept is 1.

This would also be where the graph starts on the y-axis if we were to plot all of the coordinates.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

• Slope: +3

• Slope: -3

• Slope: 1

Answer explanation

The pattern in the table shows the Xs going up by 1s, so we just need to focus on the Ys.

The Ys are increasing by 3, so the slope is +3.

Tags

CCSS.8.EE.B.5

• y=mx+b equation:

  y = -3x + 1

• y=mx+b equation:

  y = x + 3

• y=mx+b equation:

  y = x - 3

• y=mx+b equation:

  y = 3x + 1

Answer explanation

Putting together m = 3 and b = 1, the y=mx+b equation is y=3x+1.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

• Slope: -3

• Slope: 3

• Slope: -1

• Y-Intercept: 3

• Y-Intercept: -1

Answer explanation

The pattern in the table shows Xs going up by 1 so we can just look at the Ys and see its pattern is going up by 3, so the slope = 3.

When x=0 on the table, y=-1 so the y-intercept = -1.

Tags

CCSS.8.EE.B.5