Representations of Linear Functions

 A company estimates its total monthly expenses using the equation y = 2,000x + 3,000. Which of these graphs shows this relationship?

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CCSS.8.EE.B.5

The graph below represents the number of pint-sized containers that Luis can fill by using x pounds of raspberries. Which equation is represented by the graph?

Tags

CCSS.8.EE.B.5

The graph shows how the amount of grain in storage in a certain country is changing over time. Which equation describes the linear function graphed?

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Which graph models the equation -2x + y = -4?

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• 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.F.B.4

CCSS.HSF.LE.A.2

• 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

• Slope: Goes up ~25 for every 10 marbles (25/10 = 2.5)

• Slope: Goes down ~25 for every 10 marbles (-25/10 = -2.5)

Answer explanation

This one is a bit tricky to identify slope because the axes are not going by 1s.

We observe that the line is increasing over time, so we will have a positive slope.

From one point to the next, it looks like the points are climbing up 25 (for example, from 15 to 40 to 65).

However, the xs are moving by 10s from 0 to 10 to 20.

So the rate of change is going up by 25 for every 10 marbles.

25/10 = 2.5

Tags

CCSS.8.EE.B.5

• 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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.EE.B.6

CCSS.8.F.A.3

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