Question

select the correct graph and equation.
a seltner uses 3,600 gallons of fuel per hour while it is cruising, and there are 15,000 gallons of fuel in the seltner’s fuel tank when it begins to cruise. if y represents the amount of fuel, in thousands of gallons, remaining in the fuel tank after the seltner cruises for x hours, determine the graph of the solution set for this situation and the equation modeled by the graph.
graphs are shown here, and equations: y = (15 - 3.6) x, y = 15x - 3.6, y = 15 - 3.6x, y = (15 - 3.6)x

Explanation:

Step1: Identify the initial value and rate of change

The initial amount of fuel (in thousands of gallons) is 15 (since 15,000 gallons is 15 thousand gallons). The rate of fuel consumption is 3.6 thousand gallons per hour (since 3,600 gallons per hour is 3.6 thousand gallons per hour). So the equation should be \( y = 15 - 3.6x \), which is a linear equation with a y - intercept of 15 and a slope of - 3.6.

Step2: Analyze the graph

We need to find the graph where the y - intercept is 15 (the graph starts at (0,15) on the y - axis when x = 0, where x is time in hours) and the slope is - 3.6. The x - intercept (when y = 0) can be found by setting \( 0=15 - 3.6x \), so \( 3.6x = 15 \), \( x=\frac{15}{3.6}\approx4.17\) hours. So we look for the graph with y - intercept 15 and x - intercept around 4.17, and the equation \( y = 15 - 3.6x \).

Answer:

The correct equation is \( y = 15 - 3.6x \) and the graph should have a y - intercept of 15 (at x = 0) and an x - intercept around \( x=\frac{15}{3.6}\approx4.17 \) hours, with a slope of - 3.6.