Solve the problem. Write all linear equations in slope-intercept form.
-With $31.5 \%$ commitment, a company can clean up $40 \%$ of an oil spill. With $35.5 \%$ commitment, it can clean up $72 \%$ of an oil spill. Find a linear equation that models the percent cleanup for $x$ percent commitment.
A) $y = x + 32$
B) $y = 8 x - 212$
C) $y = 4 x + 32$
D) $y = 8 x + 212$

Question

Quizplus · Accepted Answer

To find the linear equation, we use the given points (31.5, 40) and (35.5, 72) to calculate the slope $m = \frac{72 - 40}{35.5 - 31.5} = \frac{32}{4} = 8$. Then, using point-slope form $y - y_1 = m(x - x_1)$ with one of the points, say (31.5, 40), we get $y - 40 = 8(x - 31.5)$. Simplifying, $y = 8x - 8(31.5) + 40 = 8x - 252 + 40 = 8x - 212$, which matches option B.

Solve the Problem 31.5%31.5 \%31.5% Commitment, a Company Can Clean Up 40%40 \%40%

Solve the Problem $31.5 \%$ Commitment, a Company Can Clean Up $40 \%$