The table below shows how much Joe earns, y, after working x hours. Joe’s Earnings Hours worked Money earned 4 $30 10 $75 12 $90 22 $165 The relationship between money earned and hours worked is linear. Joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75). How do the two slopes compare?

Both slopes are equal

Step-by-step explanation:

The general form of a linear function is:

y = mx + c

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

We can, thus, note that the slope is constant across the linear function.

Since we are given that the relation between the salary and hours worked is linear, therefore, the slope will be equal between any two points belonging to the function

Verification:

slope can be calculated as follows:

slope =  \frac{ y_{2} -  y_{1}  }{ x_{2} -  x_{1} }

1- In case of (4,30) and (12,90):

slope = slope =  \frac{ 90 - 30 }{ 12 - 4 }  = 7.5

2- In case of (4,30) and (10,75):

slope =  \frac{ 75 - 30 }{ 10 - 4 }  = 7.5

Hope this helps :)