Okay, let's do this step-by-step:
1) We have in-state tuition amounts and out-of-state tuition amounts for some state colleges.
2) We want to find a linear model that relates the in-state and out-of-state tuition.
3) Once we have the linear model, we can use it to predict the out-of-state tuition for an in-state tuition of $6,000.
Let's assume the data points are:
In-state tuition | Out-of-state tuition
$3,000 | $9,000
$5,000 | $11,000
$7,000 | $13,000
$9,000 | $15,000
To find the linear model:
1) Find the slope:
Slope = (Out-of-state tuition for $9,000 in-state tuition) - (Out-of-state tuition for $3,000 in-state tuition)
= $15,000 - $9,000 = $6,000
Slope = $6,000
2) Find the y-intercept:
y-intercept = Out-of-state tuition when In-state tuition = 0
= $9,000
So the linear model is:
Out-of-state tuition = Slope * In-state tuition + y-intercept
= $6,000 * In-state tuition + $9,000
To predict Out-of-state tuition for $6,000 In-state tuition:
Out-of-state tuition = $6,000 * $6,000 + $9,000
= $36,000 + $9,000
= $45,000
Rounding to the nearest choice:
Out-of-state tuition for $6,000 In-state tuition = $45,000
So the answer is c. about $12,450
Let me know if you have any other questions!