Step-by-step explanation:
First, we can define the input and output. One way of defining a relationship between x and y values is y=ax+b, with y being the output, a being the slope, b being the y-intercept, and x being the input. We can tell that, in our equation, we have
C(m) = 54 * m + 49.50. This matches up perfectly with our equation, with C(m) matching up with y and m with x. Therefore, C(m) is the output while m is the input.
Now that we know that, we can find the slope and y-intercept. The slope is what we multiply the input value with -- in this case, it's 54. The slope means that for each increase of 1 in the input, the output increases by the slope. In this case, for each increase of 1 month, the cost increases by 54.
The y-intercept is what we add the slope * input to in order to get the output. Here, we have y = ax + b. We add 49.50 at the end to a (54) * x (m), so we can say that 49.50 is our y-intercept. This means that when the input value is 0, this is our output value. Here, we can say that as m = 0,
C(m) = 54m + 49.50
C(m) = 54*0 + 49.50
cost = 49.50
