Solve the problem. Write all linear equations in slope-intercept form.
-A driver wants to gauge the fuel efficiency of her vehicle at speeds of $30 \mathrm { mph }$ and above. She notices that traveling at an average speed of $40 \mathrm { mph }$ results in a rating of $36 \mathrm { mpg }$, whereas at an average speed of $45 \mathrm { mph }$, her car rates $21 \mathrm { mpg }$. Find a linear equation to model the gas mileage y for an average speed of $x \mathrm { mph }$. Find the slope-intercept form of the equation of the line.
A) $y = - 3 x + 156$
B) $y = \frac { 1 } { 3 } x + 156$
C) $y = \frac { 1 } { 3 } x + 84$
D) $y = - 3 x + 84$

Question

Quizplus · Accepted Answer

The slope $m$ of the line can be calculated using the two given points $(40, 36)$ and $(45, 21)$ as $m = \frac{21 - 36}{45 - 40} = \frac{-15}{5} = -3$. Using the point-slope form $y - y_1 = m(x - x_1)$ with one of the points, for example, $(40, 36)$, we get $y - 36 = -3(x - 40)$. Simplifying this equation to slope-intercept form $y = mx + b$ gives $y = -3x + 156$.

Solve the Problem 30mph30 \mathrm { mph }30mph And Above She Notices That Traveling at an Average Speed Of

Solve the Problem $30 \mathrm { mph }$ And Above She Notices That Traveling at an Average Speed Of