Solve. Assume the exercise describes a linear relationship. When writing a linear equation, write the equation in
slope-intercept form.
-A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon, whereas they sell 3904 gallons on a day that they charge $1.40 per gallon. Find a linear equation that relates Gallons sold to price. Use this equation to predict the number of gallons sold at a price of $1.17 per gallon.
A)8117.6 gallons
B)8114.3 gallons
C)8121.7 gallons
D)8126.6 gallons

Question

Quizplus · Accepted Answer

To find the linear equation that relates Gallons sold (G) to price (P), we first identify two points on the line: (1.35, 4820) and (1.40, 3904). The slope (m) of the line is given by the change in gallons divided by the change in price: $m = \frac{3904 - 4820}{1.40 - 1.35} = \frac{-916}{0.05} = -18320$. Using the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$, and one of the points, say (1.35, 4820), we get $G - 4820 = -18320(P - 1.35)$. Solving for G in terms of P gives us the slope-intercept form: $G = -18320P + 24732$. To predict the number of gallons sold at $1.17 per gallon, substitute $P = 1.17$ into the equation: $G = -18320(1.17) + 24732 = 8117.6$ gallons.

Solve Assume the Exercise Describes a Linear Relationship