Representations of Linear Functions

Monica collects 150 eggs. After she sells x dozen of them, the equation y = 150 - 12x represents the number of eggs she has left. Which table below does not match this linear function?

• 
• 
• 
• 

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

• 
• 
• 
• 

Johnny spent 25 hours making kites. The table shows how many kites he had after 8 hours and 12 hours. Which equation is represented by the table?

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?

The table below shows the number of defective batteries identified in different shipments. Which linear equation shows the relationship between the total number of batteries in the shipment and the number of defective batteries?

• d = 100n

• d = 6n

• d = 0.06n

• d = 0.03n

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

• 
• 
• 
• 

• 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.

• 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.

• 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.

• 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