Question

PLEASE HELP NOW!!

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 $m=\frac{y_2-y_1}{x_2-x_1}$.

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

Then $m=\frac{1-0}{5-0}$, $\implies m=\frac{1}{5}$.

Carl's speed is $\frac{1}{5}$ miles per minute.

But we must leave our answer in miles per hour

Hence Carl's speed is $\frac{1}{5}\times 60=12$  miles per hour

After 2 hours, Carl will travel $12\times 2=24$ 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 $\frac{Rise}{Run}=\frac{300}{20}=15$

Therefore the rate is $ 15 per ticket.

If the theater sells 150 tickets, the earnings will be: $150\times 15=2,250$ dollars.