Question

An electrician charges 110 after 2 hours of work and 190 for 4 hours of work. Write a linear equation in point-slope form that represents the total cost (y) as a function of the number of hours worked (x).

Answer 1

y = 40x + 30

Explanation:

The equation for a linear function is given by:

y = mx + b;

where y and x are variables, m is the slope or rate of change of the function and b is the initial value of y at x = 0 (that is y intercept).

Let y represent the total cost and x represent the number of hours worked.

The electrician charges 110 after 2 hours of work and 190 for 4 hours of work.

Representing in coordinate form as (x, y) we get:

(2, 110) and (4, 190)

The equation of the function can be gotten using the formula:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Therefore:

`y-110=(190-110)/(4-2)(x-2)\\\\y-110=40(x-2)\\\\y-110=40x-80\\\\y=40x-80+110\\\\y=40x+30`