Question

applying the median-fit method
the table includes the size of roofs (x) and the cost to replace them (y). the summary points are (748, 7,048), (890, 8,385), and (1,001, 8,475).
using approximate values for the slope and y-intercept, what is the linear model?
y = dropdownx + dropdown

first table (area (ft²), cost ($)):
675, 6,500
748, 7,250
776, 7,048
810, 9,676
890, 7,785

second table (area (ft²), cost ($)):
904, 8,385
967, 8,578
1,001, 8,475
1,100, 8,695
(empty row at bottom)

Explanation:

Step1: Calculate slope from points

Use slope formula $m=\frac{y_3-y_1}{x_3-x_1}$ with $(x_1,y_1)=(748,7048)$ and $(x_3,y_3)=(1001,8475)$
$m=\frac{8475-7048}{1001-748}=\frac{1427}{253}\approx5.64$

Step2: Estimate y-intercept

Use point-slope form $y-y_2=m(x-x_2)$ with $(x_2,y_2)=(890,8385)$
$8385 - 5.64\times890 = 8385 - 5019.6 = 3365.4\approx3365$

Answer:

$y = 5.64x + 3365$

(Note: Rounding slope to 5.6 or 6 and intercept to a nearby whole number is also acceptable for approximation; 5.6x + 3400 or 6x + 3000 are reasonable alternate approximate models, but 5.64x + 3365 is the precise calculation from the given summary points.)