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

Answer:

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:

$m=\frac{y_2-y_1}{x_2-x_1}$.

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

First calculate the slope:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{450-400}{5-4} =50$.

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