ramona's garage charges the following labor rates. all customers are charged for at least 0.5 hr.

ramona's garage
hours
0.5
1
1.5
2
2.5
labor
$60
$90
$120
$150
$180

a. write a linear function for the data in the table.
b. a repair job took 4 hr and 15 min and required $390 in parts. what is the total cost?

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 =

  = 60  ----------------(2)

Now, putting the value of m and the point (x,y) = (0.5, 60) in (1), we get,

$

⇒ 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

= hour

= 4.25 hour in (4), we get,

 [in $]

= $ 285

So, the total cost of the repair job,

= $ (285 + 390)

= $ 675

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b