Question

A company is paying a local radio station to run its commercials. The cost for running commercials is a one-time campaign fee and also a per-second fee for the air time of each commercial. The cost can be modeled by the equation y = 250 + 100x where x is seconds. What is the slope and what does it represent? A. 250; it represents the per-second fee of air time B. 250; it represents the one-time campaign fee C. 100; it represents the one-time campaign fee D. 100; it represents the per-second fee of air time

Answer 1

This equation is linear, which means that it goes up by the same amount every time you increase X by one. The general form of a linear equation is y=m∗x+b where m is the slope and b is the y-intercept. The y-intercept indicates where the equation starts at x=0. In this case, it's 250, meaning that buying the commercial slot cost $250. m, on the other hand, is the slope of the graph. Here we have 100, meaning that it costs $100 per second to run the commercial. This can be visualized like so:y(0)=100∗0+250=250y(1)=100∗1+250=350As you can see, the cost went up by $100 after one second. In general, the slope represents the amount added per time, whilst the y-intercept represents the initial amount.