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

Cost per night: 75

Equation:
`y = 75x + 50`

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) = (y_2 - y_1)/(x_2 - x_1) = (350 - 200)/(4 - 2) = (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`