Final answer:
It is possible to graph the line using the points (15, 0) and (0, -75), with the latter being the y-intercept and the former indicating a point where the y-value becomes zero. Together they provide a visual representation of the nonproportional relationship depicted by the car wash equation, y = 5x - 75.
Step-by-step explanation:
Yes, it is possible to graph the line that represents the equation y = 5x - 75 by using the two points (15, 0) and (0, -75). To graph a line accurately, you only need two points through which the line passes.
These points are sufficient to establish the position and slope of the line.
The point (0, -75) is known as the y-intercept because it is where the line crosses the y-axis.
The other point, (15, 0), indicates that after a certain value on the x-axis, specifically 15 units, the y-value of the line becomes zero.
Together, these points help us plot the line: start by marking the y-intercept at (0, -75) on the graph, then move to the second point at (15, 0) and draw a straight line through these two points.
This will give you the graph of the line representing the car wash equation.
Reading graphs is essential in understanding economic relationships, and a straight line graph can illustrate such relationships clearly. In this case, the equation y = 5x - 75 displays a nonproportional relationship because of the presence of the y-intercept (-75).
Hence, the slope, which is the coefficient of x (in this case, 5), confirms that for each unit increase in x, y increases by 5 units, until the cost is covered by reaching the break-even point at (15, 0).