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This graph shows a proportional relationship.

What is the constant of proportionality?

Enter your answer as a decimal in the box.

First quadrant linear graph titled Freds Wages. Horizontal axis is labeled Hours worked with a range of 0 to 7, marked in increments of 1. Vertical axis is labeled Wages earned, in dollars and has a range of 0 to 90, marked in increments of 10. The points plotted and labeled on the graph are left parentheses 2 comma 27.60 right parentheses and left parentheses 6 comma 82.80 right parentheses.

Respuesta :

From the given two points the graph of the proportional relationship

function can be obtained.

Correct response:

  • The constant of proportionality is 13.80

Methods used to find the constant of proportionality

The given parameters are;

Range of horizontal axis = 0 to 7

Label of horizontal axis = Hours worked

Range of vertical axis = 0 to 90

Label of vertical axis = Wages earned in dollars

Points plotted are; (2, 27.60), and (6, 82.80)

Required to find the constant of proportionality

Solution:

The variables of hours worked, x, and wages earned y are proportional

when they can be expressed in the form;

y = c·x

Such that we have; Δy = c·Δx

Where;

Δy = Change in the y variable

Δx = Change in x variable

Therefore;

[tex]\displaystyle c = \mathbf{ \frac{\Delta y}{\Delta x} }[/tex]

The constant of proportionality is therefore given by the rate of change of the graph which is found as follows;

[tex]\displaystyle Rate \ of \ change = \frac{82.80 - 27.60}{6 - 2} = \mathbf{13.8}[/tex]

The rate of change indicates that for each increase of 1 hour in the hours worked, the wage increases by $13.8.

By verification, we have;

  • When the hours worked, x = 2 hours, the wage, y = 13.8 × 2 = 27.60, which corresponds with the given point (2, 27.60)

  • When the hours worked = 6 hours, the wage, y = 6 × 13.8 = 82.80, which corresponds with the given point (6, 82.80)

Therefore;

  • The constant of proportionality, the rate of change of the wage for each unit change in the hours worked, is 13.80 (which is $13.80/hour)

Learn more about proportional relationships here:

https://brainly.com/question/11696298

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