Question

grade 7
unit 11
lesson 3 homework
name liam
date 1/7/26
period 7
use the following information for questions 1-3. a screen printer prints t - shirts at a constant rate per hour. this is shown in the graph below.
(the graph has points (30,15), (45,22.5), (80,40), (100,50), (150,75))

1. use the data in the graph to complete the following table.

t - shirts printed	30	45	80	100	150

1. what is the constant of proportionality?
2. how many minutes would it take for the screen printer to print 375 shirts?

Explanation:

Question 1

Step1: Extract data from graph

We look at the given points \((30, 15)\), \((45, 22.5)\), \((80, 40)\), \((100, 50)\), \((150, 75)\). The \(x\)-values are T - shirts printed and \(y\)-values are time in minutes. So we fill the table with these \(y\)-values corresponding to the \(x\)-values.
For \(x = 30\), \(y=15\); for \(x = 45\), \(y = 22.5\); for \(x=80\), \(y = 40\); for \(x = 100\), \(y=50\); for \(x = 150\), \(y = 75\).

Step1: Recall constant of proportionality formula

For a proportional relationship \(y=kx\) (where \(y\) is time, \(x\) is number of T - shirts, and \(k\) is the constant of proportionality), \(k=\frac{y}{x}\).

Step2: Calculate \(k\) using a point

Let's use the point \((30,15)\). Then \(k=\frac{15}{30}=0.5\). We can check with another point, say \((45,22.5)\), \(\frac{22.5}{45}=0.5\), or \((80,40)\), \(\frac{40}{80}=0.5\).

Step1: Use the proportional relationship

We know that \(y = kx\), where \(k = 0.5\) (from question 2) and \(x = 375\) (number of T - shirts).

Step2: Calculate time \(y\)

Substitute \(x = 375\) and \(k=0.5\) into \(y=kx\). So \(y=0.5\times375 = 187.5\) minutes.

Answer:

T - shirts printed	30	45	80	100	150

Question 2