Representations of Linear Functions

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.

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.

• X: 2 hours per day

  Y: 34 hours

• X: total hours played

  Y: days playing 2 hours

• X: days playing 2 hours

  Y: total hours played

Answer explanation

The x is the first variable that's changing, which is determined by how many DAYS Mario plays for 2 hours extra.

The y is the outcome, which is the total amount of hours he will have played over time.

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.

Evaluate responses using AI:

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Answer explanation

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

Describe how you can find the y-intercept using the table.

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Answer explanation

Since the y-intercept is when x=0, we locate Year 0. Although the weekly paycheck is blank, we can go backwards using the pattern in the table. You should have noticed that the table is increasing by 50 every year, so if we go backwards from 400 at Year 1, we can see that the paycheck at Year 0 would be 400 - 50 = 350.

What is the X?

What is the Y?

What is the y=mx+b equation?

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Answer explanation

X is the FIRST row of the table, so it is Year.

Y is the SECOND row of the table, so it is Weekly Paycheck.

X affects Y so this shows that depending on which Year it is, it will affect what the Weekly Paycheck is.

Putting together m = 50 and b = 350, the y=mx+b question is y=50x + 350 OR y=350 + 50x.

• 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.