The linear equation shown in the graph is Slope: 7.5, cost increases by $7.50/hour. Y-intercept: 0, initial cost is $0.
To determine the slope (rate of change) and the y intercept (initial value) of the graph, we can use the following steps:
1. Choose two points on the line.
2. Calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the two points chosen.
3. Calculate the y-intercept using the formula:
b = y - mx
where (x, y) is any point on the line.
1: Choose two points on the line.
Let's choose the points (2, 15) and (4, 30).
2: Calculate the slope using the formula.
m = (30 - 15) / (4 - 2) = 15 / 2 = 7.5
3: Calculate the y-intercept using the formula.
b = 15 - 7.5 * 2 = 0
Therefore, the slope of the line is 7.5 and the y-intercept is 0.
This means that the rate of change of the cost of the child care service is $7.50 per hour. The initial value of the cost is $0.
In other words, for every additional hour of child care service, the cost increases by $7.50. The initial cost of the first hour of child care service is $0.