(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?
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.