Question

The graph shows the cost of parking, y , per hour, x , at a parking garage. The graph is titled Parking Rates. The X-axis is labeled Number of Hours and goes from zero to four by a scale of one. The y-axis is labeled Cost in dollars and goes from zero to eighteen by a scale of two. Five points are shown on the graph. Zero hours, zero dollars. One hour, four dollars. Two hours, eight dollars. Three hours, twelve dollars. Four hours, sixteen dollars. Which equation represents the relationship shown in the graph?

Answer 1

The relationship shown in the graph represents a linear equation because the cost of parking increases at a constant rate per hour. To find the equation that represents this relationship, we can use the slope-intercept form of a linear equation:

\[y = mx + b\]

Where:
- \(y\) is the cost in dollars (the dependent variable).
- \(x\) is the number of hours (the independent variable).
- \(m\) is the slope, which represents the rate of change.
- \(b\) is the y-intercept, which represents the initial cost when \(x\) is zero.

Based on the points provided in the graph:

Point 1: (0 hours, 0 dollars) gives us the y-intercept, so \(b = 0\).

Point 2: (1 hour, 4 dollars) allows us to find the slope (\(m\)) as follows:

So, the equation that represents the relationship shown in the graph is:

\[y = 4x\]

This equation represents a linear relationship where the cost (\(y\)) is directly proportional to the number of hours (\(x\)) at a rate of $4 per hour.