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

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 and

i,e    ......[1]

, where m is the slope which is given by:

.

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

First calculate the slope:

.

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

Use distributive property on RHS ( i.e, )

Now, add 400 to both sides of an equation:

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

except a rational number. : )