Question

I do not understand how to use the table to determine the correct answer.

Answer 1

The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.

Step-by-step explanation:

We'll use the below formula to determine the slope of the line;

`m=(y_2-y_1)/(x_2-x_1)`

Let's go ahead and compute the slope between (4, 30) and (12, 90) using x1 = 4, y1 = 30, x2 = 12, and y2 = 90.

Substituting the above values into our formula, we'll have;

`m=(90-30)/(12-4)=(60)/(8)=(15)/(2)=7.5`

Let's now compute the slope between (4, 30) and (10, 75) using x1 = 4, y1 = 30, x2 = 10, and y2 = 75.

Substituting the above values into our formula, we'll have;

`m=(75-30)/(10-4)=(45)/(6)=(15)/(2)=7.5`

We can see from the above that the slope between (4, 30) and (12, 90) and (4, 30) and (10, 75) is equal and this is so because the relationship between money earned and hours worked, as we're told in the question, is linear. Therefore, it should have a constant slope.