Question

I need to find out the cost per lamp, the linear equation and the total cost of making 8560 lamps

Answer 1

The cost per lamp is the slope of the line of cost.

The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

`m=\frac{y_2-y_1_{}}{x_2-x_1}`

In this case, the x-variable represents the number of lamps and the y-variable represents the cost.

This line passes through the points (19, 2000) and (22, 2240), then its slope is:

`m=(2240-2000)/(22-19)=(240)/(3)=80`

The cost per lamp is $80.

The equation of a line in slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting with the point (19, 2000) and m = 80, we get:

2000 = 80*19 + b

2000 = 1520 + b

2000 - 1520 = b

480 = b

Therefore, the linear equation is (y-variable is replaced by C):

C = 80x + 480

Substituting C = 8560 and solving for x, we get:

8560 = 80x + 480

8560 - 480 = 80x

8080 = 80x

8080/80 = x

101 = x

They made 101 lamps.