Decide whether each table could represent a proportional relationship. In the essay box explain if the relationship could be proportional, what would be the constant of proportionality?

Annie’s Attic is giving away $5 off coupons.

Answer:

This table does represent a proportional relationship because the sale price and original price are going up at the constant rate of 10

Step-by-step explanation:

The equation of line is y = -x + 25 and the constant of proportionality is 5

A line's equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Furthermore, y - y1 = m (x - x1).

y = second point's y-coordinate

y1 = point one's y-coordinate m = slope x = point two's x-coordinate

x1 = point one's x-coordinate

The slope is m = (y2 - y1) / (x2 - x1).

Given the data,

Let the line equation be written as A.

The value of A is now

Let P be the initial point ( 15 , 10 )

Let's call the second point Q. ( 25 , 20 )

The slope of the line is now m = (y2 - y1) / (x2 - x1).

m slope = [tex]\frac{(20-10)}{(25-15)}[/tex]

m slope = [tex]\frac{-10}{10}[/tex]

m slope = -1

The equation for the line is now y - y1 = m (x - x1).

y - 10 = -1 ( x - 15 )

Simplifying the equation yields y - 10 = -x + 15.

We get y = -x + 25 by adding 10 to both sides of the equation.

So, if the selling price x is $10, the original price y is $ 15.

Hence , the equation of line is y = -x + 25 and the constant of proportionality is 5

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