Barry is organizing a holiday party and researching the cost of invitations the table shows the total cost, y, for a given number of imitations, x. Number of invitations, x. 10, 20, 30, 40, total cost, y ($) 29, 54, 79, 104, which equation describes the relationship between the number of invitations and the total cost?

Question

A. Y = 5/2x - 4
B. Y = 10/3x - 4
C. Y = 2/5x + 4
D. Y = 5/2x + 4

Answer 1

To find the equation that describes the relationship between the number of invitations and the total cost, we can use the given data to determine the slope and y-intercept.

First, we can find the slope by calculating the change in y divided by the change in x:
Slope = (Change in y) / (Change in x)

Slope = (54 - 29) / (20 - 10) = 25 / 10 = 5/2

Next, we can use the slope-intercept form of a linear equation (y = mx + b) to find the y-intercept. We substitute one set of values from the table into the equation and solve for b:
29 = (5/2)(10) + b
29 = 25/2 + b
29 - 25/2 = b
(58 - 25)/2 = b
33/2 = b

So the equation that describes the relationship between the number of invitations and the total cost is:

Y = 5/2x + 33/2

However, none of the given answer choices match this equation.