Question

Egbert charges a fixed rate plus an hourly rate to bill clients. It costs $100 for a job that is 3 hours of work. This is expressed as an ordered pair (3, 100). a) He charges $190 for 13 hours of work. Express this as an ordered pair. b) Find the slope between these 2 points. What does the slope represent in terms of Egbert’s fees? c) Write a linear equation to represent this scenario where x is the number of hours and y is the total charges.

Answer 1

a. 9

b. Slope represents charges of job per hour of work

c. y = 9x + 73

Explanation:

a. $190 charges for 3 hours of work

As an ordered pair, this could be written as;

(13,190)

b. slope between (3,100) and (13,190)

Mathematically, that would be;

m = (y2-y1)/(x2-x1)

Thus, m will be ;

m= (190-100)/(13-3) = 90/10 = 9

So what does this represent? In mathematical terms, the slope is the rate of change of the value on the y-axis to the value on the x-axis.

In this case, it is the charges of job per hour of work

c. For a straight line plot , the equation can be written as;

y = mx + c

where m is the slope of the line and c is the y-intercept

in this case we have ;

y = 9x + c

Where the value 9 is the slope.

Now to get the value of c, we can use any of the points; let’s use (3,100)

Thus;

100 = 9(3) + c

c = 100-27

c = 73

So the linear equation would be;

y = 9x + 73