Question

Crew B earns $315 after 3 hours, $525 after 5 hours, and $735 after 7 hours of work. Explain wheter or not crew B's data shows a proportional relationship. If the data are proportional, identify the constant of proportionality.

Answer 1

Explanation:

`(315)/(3)=105\\(525)/(5)=105\\(735)/(7)=105\\`

constant of proportionality=105

as the proportion is same ,so they are in proportional relationship.

Answer 2

the data shows a proportional relationship with constant of proportionality $105/hr.

Explanation:

Here we have the coordinates of three points and want to know whether these points are collinear (that is, whether or not they lie on the same line). In other words, is the slope of the line segment connecting (3, $315) and (5, $525) the same as that of the line segment connection (5, $525) and (7, $735)?

Let's find the slope of the line segment connecting (3, $315) and (5, $525):

m = (change in y) / (change in x) = ($525 - $315) / (5 - 3) = $105/hr

Next, find the slope of the line segment connecting (5, $525) and (7, $735):

m = $210/(2 hr) = $105/hr

Because the slopes of these two line segments are the same, we conclude that the three points are collinear and that the data shows a proportional relationship with constant of proportionality $105/hr.