Representations of Linear Functions

• Slope: 0

• Y-Intercept: 0

• Slope: 1

• Y-Intercept: 1

Answer explanation

The table is going by 1s on both the Xs and the Ys, so the slope is 1.

When x=0, y=0, so the y-intercept is 0.

• Slope: 5

• Slope: -2

• Slope: 2

• Y-Intercept: -2

• Y-intercept: 5

Answer explanation

The graph is going down from left to right, so it will have a negative slope. It is going down 2 for every single change in x, showing a slope of -2.

The graph starts on the y-axis at 5, so the y-intercept is 5.

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.

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.

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.

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.

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.

Slope:

Answer explanation

The rate of change in this word problem is 2 since Mario is playing 2 more hours A day.

Key words are often "each," "every," "a," and other words that hint at a constant change.

Select ALL correct equivalent equations.

• y=mx+b equation:

  y = 2x + 34

• y=mx+b equation:

  y = 34x + 2

• y=mx+b equation:

  y = 34 + 2x

• y=mx+b equation:

  y = 2 + 34x

Answer explanation

As long as the equation contains 2x and 34, you can arrange the terms in either order.

The 2 must be connected to x since Mario is playing 2 hours, but we don't know for how many days.

The 34 must be by itself because it's the starting amount of hours and should only be added once.

Describe how you can identify the slope in the table.

Answer explanation

For every year, how do you see the weekly paycheck changing? What is the pattern?