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.