Question

use the graph to write an equation of the line.
y =
interpret the slope.
the fuel decreases 30 gallons for every mile driven.
the fuel decreases 12 gallons for every mile driven.
gasoline tank
fuel (gallons)
distance (miles)

Explanation:

Step1: Find the slope formula

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Here, let $(x_1,y_1)=(0,90)$ and $(x_2,y_2)=(90,9)$.

Step2: Calculate the slope

$m=\frac{9 - 90}{90-0}=\frac{- 81}{90}=-\frac{9}{10}=-0.9$.

Step3: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the graph, when $x = 0$, $y=90$, so $b = 90$.

Step4: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m=-0.9$ and $b = 90$ into the formula, we get $y=-0.9x+90$.

Step5: Interpret the slope

The slope $m=-0.9$ means that for every 1 unit increase in $x$ (distance in miles), $y$ (fuel in gallons) decreases by 0.9 gallons. In terms of the given options, we can also note that if we consider the change in a more general sense, the fuel level is decreasing as the distance is increasing.

Answer:

$y=-0.9x + 90$; None of the given options for slope - interpretation are correct as the slope is $-0.9$ which means the fuel decreases 0.9 gallons for every mile driven.