Really need some math help

When an employee works 33 hours, she/he earns $246.18. When she works 36 hours, she earns $268.56. Write a linear function for her earnings E as a function of hours worked, h.

a. E(h) = 0.13h

b. E(h) = 0.13h + 246.18

c. E(h) = 7.46h

d. E(h) = 7.46h + 246.18 <--- I think this is the answer? Am I correct? Please explain! I am really confused!

The answer you picked says:
The earnings of this person are
1) $7.46 per hour (7.46h)
2) plus an additional $246.18 added. ( ???)

The right answer is:
The person makes $7.46 per hour (with nothing added)

Check
33 hours @ $7.46 per hour = $246.28 ✔
36 hours @ $7.46 per hour = $268.56 ✔
~~~~~~~~~~~~~~~~~
Answer:
c. E(h) = 7.46h
This equation means:
Earnings = ( $7.46 ) × ( the number of hours (h) worked )

So first you need to find the rate per hour (like finding the slope of a line).

Since you have two different time periods, you can calculate the hourly rate by looking at how the total pay changed with the difference in hours worked. So (change in total pay) / (change in hours) = hourly rate.

Rate = (268.56 - 246.18) / (36 - 33) = 22.38 / 3 = 7.46 per hour.

To find out if there is any constant added (like a y-intercept), check to see if you need any.

Let E(h) = 7.46h + C, then plug in E(h) = 268.56 and h = 36, we find C = 0. Try the same for E(33) = 246.18, and C = 0, so your answer should be

c. E(h) = 7.46h

You have the following 2 points
(33, 246.18)
(36, 268.56)

Calculate the slope with m = (y2-y1)/(x2-x1)

m = (268.56-246.18)/(36-33)
m = 7.46

Now use the point-slope formula (y - y1)=m(x-x1)
y - 246.18 = 7.46(x - 33)
y - 246.18 = 7.46x - 7.46(33)
y - 246.18 = 7.46x - 246.18
y = 7.46x

ANS C

h₁ = 33
y₁ = 246.18

h₂ = 36
y₂ = 268.56

m = (y₂ - y₁) / (h₂ - h₁):

m = (268.56 - 246.18) / (36 - 33)
m = 22.38 / 3
m = 7.46

b = y₁ - m(x₁):

b = 246.18 - 7.46(33)
b = 246.18 - 246.18
b = 0

Equation:

E(h) = 7.46x

Answer: Option c
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E(h) = a * h

E(33) = 33a = 246.18
=> a = 7.46

it works for h = 36:
E(36) = 7.46 * 36
E(36) = 268.56

E(h) = 7.46 h

246.18/33 = 7.46
268.56/36 = 7.46
E(h) = 7.46h (c)

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