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?

If we rewrite this equation, it would look like this: , 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  , and .  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.