The cost , in dollars, to rent a carpet-cleaning machine for hours is modeled by the equation
When the equation is graphed with on the horizontal axis and on the vertical axis, which of the following best represents the meaning of the -intercept in this context?
An intercept is where a graph meets an axis. For a -intercept, identify the input and output at the vertical-axis crossing. Graph the cost model in Desmos using for hours and for cost, then read its vertical-axis crossing. Don't confuse the dollars added per hour with the cost at that crossing.
Hints
- Hint 1
A -intercept is a point on the vertical axis, so start where the line crosses that axis. What does the horizontal coordinate mean at that crossing?
- Hint 2
The multiplying the hours is a rate: it tells you how many dollars each additional hour adds. The intercept is a point, so read its hours and its cost together.
Step-by-step
Read the vertical-axis crossing
Step 1Identify the hours at the intercept
An intercept is where a graph meets an axis. At the -intercept, the graph meets the vertical axis, so its horizontal coordinate is . Since the horizontal axis measures , this point represents hours.
- Step 2
Read the cost at that point
Type in Desmos, using for and for . Click the line, then its vertical-axis crossing. Desmos shows : the model gives a cost of $75 for hours. The is the hourly rate, not the cost at the intercept. The -intercept pairs zero hours with the cost at zero hours. So the answer is the total cost to rent the machine for hours. Choice B.