Question

Finn suggests that club members walk dogs for a fee. He proposes they offer 5 walks for $20 and 10 walks for $40 per dog. Write an equation to represent the amount earned, y, for x number of walks. Then graph the function

Answer 1

The equation to represent the amount earned, y, for x number of walks.

`y = 4x`

The graph of the function is attached below.

Explanation:

• Let 'y' be the amount earned

• Let 'x' be the number of walks

We know that the slope-intercept form of the line equation is

`y = mx+b`

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

Given that Finn suggests that club members walk dogs for a fee. Thus, the y-intercept is 0. i.e. b = 0

Given that he proposes they offer 5 walks for $20 and 10 walks for $40 per dog.

Thus, the rate of change of function or slope = (40-20) / (10 - 5)

= 20 / 5

= 4 dollars per walk

so, rate of change = slope = m = 4

Now substitutng m = 4 and b = 0 in the slope-intercept form of the line equation

`y = mx+b`

`y = 4x + 0`

`y = 4x`

Therefore, the equation to represent the amount earned, y, for x number of walks.

`y = 4x`

The graph of the function is attached below.