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 [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
i,e [tex]y-y_1 =m(x-x_1)[/tex] ......[1]
, where m is the slope which is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
For the given points (4, 400) and (5, 450);
First calculate the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{450-400}{5-4} =50[/tex].
Now, put this value of m in equation [1] ;
[tex]y-400=(50)(x-4)[/tex]
Use distributive property on RHS ( i.e, [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex])
[tex]y-400=50x-200[/tex]
Now, add 400 to both sides of an equation:
[tex]y-400+400=50x-200+400[/tex]
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
