Question

i-ready
understand proportional relationships — instruction — level g
the graph shows the amount of money nationwide shipping company pays
its drivers for miles driven at work.
complete each statement.
the amount drivers are paid per mile
is the same for each
distance, so the relationship is
proportional.
the constant of proportionality is
blank.
graph titled driver pay with x-axis miles driven (0 to 500) and y-axis pay (dollars) (0 to 200), with points plotted. also a number pad is shown.

Explanation:

Step1: Identify a point on the graph

Looking at the graph, we can take the point (100, 40) where miles driven (x) is 100 and pay (y) is 40 dollars.

Step2: Calculate the constant of proportionality

The constant of proportionality \( k \) in a proportional relationship \( y = kx \) is calculated as \( k=\frac{y}{x} \). Substituting \( x = 100 \) and \( y = 40 \), we get \( k=\frac{40}{100}=0.4 \). We can verify with another point, say (250, 80): \( \frac{80}{250} = 0.32 \)? Wait, no, maybe I picked the wrong point. Wait, let's check the grid. Wait, the x - axis: 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500. The y - axis: 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200. Let's take (100, 40): \( \frac{40}{100}=0.4 \), (250, 80): \( \frac{80}{250}=0.32 \)? No, that can't be. Wait, maybe (250, 80) is wrong. Wait, looking at the graph, the first point is at (100, 40), then (250, 80)? Wait, no, 250 on x - axis, y is 80? Wait, 100 miles: 40 dollars, 250 miles: 80 dollars? Wait, \( \frac{40}{100}=0.4 \), \( \frac{80}{250}=0.32 \). That's a problem. Wait, maybe I misread the graph. Wait, let's check the x - axis labels. Wait, the x - axis: each grid is 50? Wait, 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500. The y - axis: 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200. Let's take (100, 40): \( \frac{40}{100}=0.4 \), (250, 80): no, 250 is 2.5 times 100, 80 is 2 times 40. Wait, that's not proportional. Wait, maybe the points are (100, 40), (250, 80) is wrong. Wait, maybe the second point is (200, 80)? Wait, no, the graph: let's see, the first dot is at (100, 40), then next at (250, 80)? Wait, no, 100 to 250 is 150 miles, 40 to 80 is 40 dollars. Wait, maybe I made a mistake. Wait, the constant of proportionality is \( \frac{y}{x} \). Let's take (100, 40): \( \frac{40}{100}=0.4 \), (250, 100)? No, 250 on x, y is 100? Wait, no, the third dot is at (350, 120)? Wait, no, the user's graph: "Driver Pay" graph. Let's re - examine. The x - axis is miles driven, y - axis is pay in dollars. Let's take the point (100, 40): so for 100 miles, pay is 40. So \( k=\frac{40}{100}=0.4 \). Let's check another point: (250, 100)? No, 250 miles, pay is 100? Wait, no, the grid: 100 miles: 40, 250 miles: 100? Wait, 250 - 100 = 150 miles, 100 - 40 = 60 dollars. \( \frac{60}{150}=0.4 \). Ah, I see, I misread the y - value for 250. So (250, 100) is wrong, (250, 100) would be \( \frac{100}{250}=0.4 \). Wait, the dot at 250: y is 100? Wait, the y - axis: 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200. So 100 is a grid line. So (100, 40), (250, 100)? No, 250 is 2.5 times 100, 100 is 2.5 times 40. Yes, \( 40\times2.5 = 100 \), \( 100\times2.5=250 \). So \( k = \frac{40}{100}=0.4 \), \( \frac{100}{250}=0.4 \), \( \frac{120}{300}=0.4 \) (if 300 miles, pay is 120), \( \frac{150}{375}=0.4 \)? Wait, no, 350 miles: pay is 140? Wait, \( \frac{140}{350}=0.4 \). Yes, so the constant of proportionality is \( \frac{pay}{miles}=\frac{40}{100}=0.4 \) (or \( \frac{100}{250}=0.4 \), \( \frac{140}{350}=0.4 \), \( \frac{120}{300}=0.4 \)). So the constant of proportionality is 0.4 (or \( \frac{2}{5} \) or 0.4 dollars per mile).

Answer:

0.4 (or \( \frac{2}{5} \))