15. VIDEO RENTALS A video store charges $$ \$ 10 $$ for a rental card plus $$ \$ 2 $$ per rental. a. Write an equation in slope-intercept form for the total cost c of buying rental card and renting $$ m $$ movies. b. Graph the equation.

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To solve the problem, we need to write an equation that represents the total cost $$ c $$ of buying a rental card and renting $$ m $$ movies.

### a. Write the equation in slope-intercept form

The total cost $$ c $$ can be expressed as the sum of the cost of the rental card and the cost of renting $$ m $$ movies.

1. The cost of the rental card is $$ \$10 $$.
2. The cost of renting $$ m $$ movies is $$ \$2 $$ per movie, which can be expressed as $$ 2m $$.

Thus, the total cost $$ c $$ can be written as:

$$
c = 10 + 2m
$$

This equation is already in slope-intercept form, which is $$ y = mx + b $$, where:
- $$ m $$ (the slope) is $$ 2 $$ (the cost per movie),
- $$ b $$ (the y-intercept) is $$ 10 $$ (the cost of the rental card).

### b. Graph the equation

To graph the equation $$ c = 10 + 2m $$:

1. **Identify the y-intercept**: The y-intercept is $$ 10 $$. This means that when $$ m = 0 $$ (no movies rented), the total cost $$ c $$ is $$ 10 $$.
2. **Identify the slope**: The slope is $$ 2 $$, which means for every additional movie rented, the total cost increases by $$ 2 $$.

**Plotting points**:
- When $$ m = 0 $$: $$ c = 10 $$ (point: $$ (0, 10) $$)
- When $$ m = 1 $$: $$ c = 10 + 2(1) = 12 $$ (point: $$ (1, 12) $$)
- When $$ m = 2 $$: $$ c = 10 + 2(2) = 14 $$ (point: $$ (2, 14) $$)
- When $$ m = 3 $$: $$ c = 10 + 2(3) = 16 $$ (point: $$ (3, 16) $$)

**Graph**:
- Plot the points $$ (0, 10) $$, $$ (1, 12) $$, $$ (2, 14) $$, and $$ (3, 16) $$.
- Draw a straight line through these points, extending it in both directions.

The graph will show a straight line starting at $$ (0, 10) $$ and rising with a slope of $$ 2 $$.

### Summary
The equation for the total cost of renting movies is $$ c = 10 + 2m $$, and the graph is a straight line with a y-intercept at $$ 10 $$ and a slope of $$ 2 $$.
The equation for the total cost is $$ c = 10 + 2m $$. The graph is a straight line with a y-intercept at $$ 10 $$ and a slope of $$ 2 $$.

15. VIDEO RENTALS A video store charges \( \$ 10 \) for a rental card plus \( \$ 2 \) per rental. a. Write an equation in slope-intercept form for the total cost c of buying rental card and renting \( m \) movies. b. Graph the equation.

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