Question

The amount that a consultant charges for her work can be modeled using a linear function for 4 hours of work the consulatant charges $400 for 5 hours she charges $450 write the function f(h) that represents the amount the consultant charges for h hours of work

Answer 1

Let the amount of consultant charges be y

and let the hours of work be x.

From the given condition, we have

(4, 400) and (5, 450)

Use Slope intercept form for two points
`(x_1, y_1)` and
`(x_2, y_2)`

i,e
`y-y_1 =m(x-x_1)` ......[1]

, where m is the slope which is given by:

`m=(y_2-y_1)/(x_2-x_1)`.

For the given points (4, 400) and (5, 450);

First calculate the slope:

`m=(y_2-y_1)/(x_2-x_1)=(450-400)/(5-4) =50`.

Now, put this value of m in equation [1] ;

`y-400=(50)(x-4)`

Use distributive property on RHS ( i.e,
`a \cdot (b+c) = a\cdot b+ a\cdot c`)

`y-400=50x-200`

Now, add 400 to both sides of an equation:

`y-400+400=50x-200+400`

Simplify:

y = 50x+200.

or

f(x) = 50x+200, where x be the hours of work.

Therefore, the function that represents the amount the consultant charges for h hours of works ;

f(h) = 50h+200