Question

A park volunteer plans to work on the park's stone walls for 1 hour every Monday, 1 hour every

Wednesday, and 3 hours on Fridays. The graph shows the number of hours he plans to work for a
given number of weeks. Complete parts a through c.

Answer 1

The answer is below

Explanation:

A linear graph has an equation in the form y = mx + b, where y and x are variables, m is the slope of the line and b is the y intercept (that is value of y at x = 0).

a) y represent the number of hours worked and x represent the number of weeks. The points are represented in the form (x, y).

First we can find the slope of the line by picking two points from the graph. Let us use (0, 0) and (2, 10). The slope m is given as:

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(10-0)/(2-0) \\\\m=5`

The slope and constant of proportionality is 5.

b) The equation can be gotten using the points (0, 0) and (2, 10). Therefore:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\y-0=(10-0)/(2-0)(x-0)\\\\y=5x\\\\`

c) In 16 weeks (i.e. x = 16):

y = 5x

y = 5(16)

y = 80 hours