Question

Sam takes part in a car race that has 20 laps. He completes 4 laps every 3 minutes. The number of laps Sam has left to drive after x minutes is represented by the function f(x) = 20 − (4/3)(x). Identify the graph that describes this function and its intercepts. What does each intercept represent?

Answer 1

If we rewrite this equation, it would look like this: $y=- \frac{4}{3}x+20$, which is the equation for a straight line with a slope of -4/3 and a y-intercept of 20.  The y-intercept exists when x = 0.  "x" represents the number of minutes he drives, "y" represents the number of laps he drives.  Slope is rise/run, or y/x, which gives us that he drives 4 laps in 3 minutes (the slope of our line).  The y-intercept, when x = 0, tells us that when he has driven 0 minutes, or hasn't driven at all yet, he still has 20 laps to go.  When y = 0, the x-intercept is  $0=- \frac{4}{3}x+20$, and $-20=- \frac{4}{3} x$.  Multiply both sides by 3 to get that -60 = -4x and that means that x is 15.  This means that from start to finish, it takes him 15 minutes to drive the 20 laps.