Question

proportional relationships
below is an example of a proportional relationship in the form of a verbal description, table,
graph and equation. the constant of proportionality is given in the middle. circle where you
see the constant of proportionality in each form. then, create your own proportional
relationship and write it in the form of a verbal description, table, graph and equation.
verbal description
pedro went to the market
and bought one pound (p)
of apples for $2.50 (d).
table
p 1 2 3 4
d 2.50 5.00 7.50 10.00
graph
equation
d = 2.5p
verbal description
table
graph
equation

Explanation:

Step1: Create a proportional relationship

Let's say: "A factory produces widgets. The number of widgets (w) produced is proportional to the number of hours (h) worked. Each hour, 3 widgets are produced."

Step2: Create a table

h	1	2	3	4

Step3: Create a graph

Plot the points (1,3), (2,6), (3,9), (4,12) on a coordinate plane where the x - axis is for \(h\) (hours) and the y - axis is for \(w\) (widgets). The graph will be a straight line passing through the origin.

Step4: Create an equation

The general form of a proportional relationship is \(y = kx\). Here, \(w\) is \(y\), \(h\) is \(x\), and \(k = 3\). So the equation is \(w=3h\).

Answer:

• Verbal Description: "A factory produces widgets. The number of widgets (w) produced is proportional to the number of hours (h) worked. Each hour, 3 widgets are produced."
• Table:

h	1	2	3	4

• Graph: Plot points (1,3), (2,6), (3,9), (4,12) on a coordinate plane (x - axis: \(h\), y - axis: \(w\)) and draw a straight - line through them (passing through the origin).
• Equation: \(w = 3h\)