(0,8)----------(3,20)

Colin charges a flat fee for plus an hourly fee. His total cost is represented on the graph. How can you represent this situation algebraically?

1 answer

Let's represent the flat fee as "a" and the hourly fee as "b".

The equation of a straight line on a graph can be represented algebraically as y = mx + c, where m is the slope of the line and c is the y-intercept.

In this case, the slope of the line represents the hourly fee, and the y-intercept represents the flat fee.

Given the points (0, 8) and (3, 20), we can find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)
= (20 - 8) / (3 - 0)
= 12 / 3
= 4

Now, we can substitute the slope value (m) into the equation y = mx + c, and use one of the given points to find the value of c:

Using the point (0, 8), we have:
8 = 4(0) + c
c = 8

So the equation of the line is:
y = 4x + 8

Therefore, the total cost (y) is represented algebraically as 4x + 8, where x represents the number of hours. The flat fee is $8 and the hourly fee is $4.