Question

Ian and his friends are renting a cabin that charges an initial fee plus a rate per night. The relationship between the cost and number of nights is shown in the graph.
What is the cost per night?

writ e an equation to represent this.

Answer 1

Answer:

Cost per night: 75

Equation: $y = 75x + 50$

Step-by-step explanation:

An equation to represent the situation can be written in the slope-intercept form, $y = mx + b$, where,

m = slope of the graph, which is the rate per night.

b = y-intercept, which is the initial fee. It is the point where the line intercepts the y-axis.

Let's find m, using two points on the line, (2, 200) and (4, 350)

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{350 - 200}{4 - 2} = \frac{150}{2} = 75$

✅The cost per night = 75

y-intercept, b, = 50. The line intercepts the y-axis at y = 50, when x = 0.

Substitute m = 75, and b = 50 into $y = mx + b$.

✅The equation would be:

$y = 75x + 50$