Question

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Question #1

Look at the following graph of Carl’s travel time and distance:


What is Carl’s constant rate of speed (in miles per hour)?

How many miles will Carl have traveled after 2 hours?


Question #2

Look at the following equation:


–4x + y = 10

What is the slope of this line?

What is the value of y when x = 3?


Question #3

What is the rate (in dollars per ticket)?

How much money will the theater earn if it sells 150 tickets?

Answer 1

1. Carl's constant rate of speed is the slope of the straight line graph.

This straight line passes through: (0,0), (5,1), (10,2) etc

We can use the slope formula with any two points to find the slope of this line.

The slope formula is
`m=(y_2-y_1)/(x_2-x_1)`.

Let
`(x_1,y_1)=(0,0)` and
`(x_2,y_2)=(5,1)`

Then
`m=(1-0)/(5-0)`,
`\implies m=(1)/(5)`.

Carl's speed is
`(1)/(5)` miles per minute.

But we must leave our answer in miles per hour

Hence Carl's speed is
`(1)/(5)* 60=12` miles per hour

After 2 hours, Carl will travel
`12* 2=24` miles.

2. The given line has equation
`-4x+y=10`

We write this in slope-intercept form by solving for y.

`\implies y=4x+10`

This is in the form
`y=mx+c`, where
`m=4` is the slope.

When x=3,
`y=4(3)+10`

`\implies y=12+10=22`

When x=3, y=22

3. The given straight line graph that models the situation passes through:

(0,0) and (20,30).

The slope of this line is
`(Rise)/(Run)=(300)/(20)=15`

Therefore the rate is $ 15 per ticket.

If the theater sells 150 tickets, the earnings will be:
`150* 15=2,250` dollars.