Respuesta :
Answer:
a. The linear function is given by,
y = 60x + 30 [y is in $ and x is in hour and x ≥ 0.5]
= 60 [for x < 0.5]
b. The total cost of the repair job is, $ 675 .
Step-by-step explanation:
Let, the linear function describing garage charge( y in $) and no. of hours of repair job ( x in hour) be,
y = mx + c [for x ≥ 0.5] -----------(1)
where, m is the slope of the line and c is the y intercept.
Now ,
m = [tex]\frac {90 - 60}{1 - 0.5}[/tex]
= 60 ----------------(2)
Now, putting the value of m and the point (x,y) = (0.5, 60) in (1), we get,
[tex]60 = 60 \times 0.5 + c[/tex] $
⇒ c = 30 ----------------- (3)
Hence, the linear function is given by,
y = 60x + 30 [y is in $ and x is in hour and x ≥ 0.5] ------------(4)
= 60 [for x < 0.5]
Now, putting
x = 4 hr 15 min
= [tex]4\dfrac {15}{60}[/tex] hour
= 4.25 hour in (4), we get,
[tex]y = 60 \times 4.25 + 30[/tex] [in $]
= $ 285
So, the total cost of the repair job,
= $ (285 + 390)
= $ 675
