Question 64·Easy·Linear Functions
The table below shows the total cost , in dollars, of hiring a math tutor for hours.
| (hours) | (dollars) |
|---|---|
| 2 | 110 |
| 5 | 200 |
Assuming the relationship between and is linear, what is the cost for each additional hour of tutoring, in dollars?
For SAT questions asking for a “cost per” or “rate per” from a linear table, quickly recognize that this is the slope: pick any two rows, subtract the outputs (costs) to get the change in cost, subtract the inputs (hours) to get the change in hours, then divide change in cost by change in hours. Avoid extra work like finding the full equation unless needed; just compute the rate directly and match it to the answer choices.
Hints
Think about what “per additional hour” means
“Per additional hour” means how much the total cost increases when the number of hours increases by 1. This is the constant rate of change in a linear relationship.
Compare the two rows in the table
Look at how much the cost changes when you go from 2 hours to 5 hours. Also note how many extra hours that is.
Use change in cost over change in hours
Once you know how much the cost increases and how many hours that increase happens over, divide the change in cost by the change in hours to get the cost per hour.
Desmos Guide
Plot the two data points
In Desmos, type the two points as (2,110) and (5,200) on separate lines. Desmos will show these points on the coordinate plane.
Use Desmos to compute the slope
In a new line, type (200-110)/(5-2) to have Desmos calculate the rate of change between the two points. The value Desmos returns is the cost for each additional hour of tutoring; choose the answer option that matches this value.
Step-by-step Explanation
Identify what is being asked
The question asks for the cost for each additional hour of tutoring. In a linear relationship, this is the rate of change, or slope: how much (cost) increases when (hours) increases by 1.
Compute the change in cost and change in hours
Use the two points from the table: and .
- Change in cost: dollars
- Change in hours: hours
So when the hours go up by 3, the cost goes up by 90.
Find the rate (slope) and match it to an answer choice
The cost per additional hour is the change in cost divided by the change in hours:
So the cost for each additional hour of tutoring is $30, which corresponds to choice B) $30.