Answer:
Steve
Greta & Richard
Explanation:
Greta:
p = 75 + 45h
The equation of her pay is:
p = 45h + 75
Compare that with
y = mx + b
Here, m = 45, and b = 75.
m, the slope, is the hourly rate Greta charges.
b, the y-intercept, is the initial charge.
In other words, if you call Greta, she charges $75 just to go there before she works any time at all. Then she charges $45 per hour.
Richard:
Look in the graph. The y-intercept is (0, 50). That means b = 50.
Now we calculate the slope using 2 points.
(0, 50), (1, 80)
slope = (difference in y)/(difference in x)
slope = m = (80 - 50)/(1 - 0) = 30/1 = 30
m = slope = 30.
Since the slope is 30, and the y-intercept is 50, that means that Richard charges $30 per hour and an initial fee of $50 just to go there.
p = 30h + 50
Steve:
Take two lines of information from Steve's table:
(3, 165), (5, 275)
Let's find the equation of a line through those two points.
m = slope = (difference in y)/(difference in x)
m = (275 - 165)/(5 - 3) = 110/2 = 55
y = mx + b
165 = 55(3) + b
165 = 165 + b
b = 0
y = 55x
p = 55h
The slope of Richard's equation is 55, so Richard charges $55 per hour. For Richard, b = 0. Since the y-intercept is zero, that means Richard does not charge an initial fee. With Richard, his total pay is only from the number of hours he works.
Now we can answer the questions.
-Who earns the most per hour, Geeta, Richard, or Steve? Explain how you found your answer.
Greta: $45/hour
Richard: $30/hour
Steve: $55/hour
Answer: Steve
-Which technician(s) have an equation for their pay with the y-intercept at a point other than (0,0)? Explain what the y-intercept(s) mean(s) in terms of this scenario.
The equation of their pay are:
Greta: p = 45h + 75
Steve: p = 30h + 50
Steve: p = 55h
Answer: Greta at 75 and Richard at 50. This means they charge those amounts before they work any time. The fee for them to come to you is the y-intercept.