Question

check your understanding
a conference center charges an initial deposit plus an hourly rate for renting the space for an event or party. the total cost for different numbers of hours, including the deposit, is shown in the graph.
rental costs
(graph with x-axis as hours (0 - 10) and y-axis as total cost (50 - 500), plotted line)
step 1 find and interpret the rate of change.
the rate of change is 25
step 2 find and interpret the initial value.
x=0, y=75 = 75
step 3 write the equation of the function in slope - intercept form.
y = 25x + 75

Explanation:

Step1: Calculate rate of change

Use two points, e.g., $(1,100)$ and $(2,125)$.
$\text{Rate of change} = \frac{125-100}{2-1} = 25$

Step2: Identify initial value

Find $y$-intercept (when $x=0$): $y=75$

Step3: Write slope-intercept equation

Slope $m=25$, intercept $b=75$.
$y = 25x + 75$

Answer:

1. Rate of change: 25, meaning the hourly rental fee is $25 per hour.
2. Initial value: 75, meaning the initial deposit is $75.
3. Equation: $y = 25x + 75$