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?
A. Y = 5/2x - 4
B. Y = 10/3x - 4
C. Y = 2/5x + 4
D. Y = 5/2x + 4
To find the equation that describes the relationship between the number of invitations and the total cost, we can use the given values to calculate the slope of the equation.
The slope of a linear equation is given by the change in y divided by the change in x.
Using the given values, we can calculate the slope between each pair of points:
Between 10 invitations and 20 invitations: (54 - 29) / (20 - 10) = 25 / 10 = 5/2
Between 20 invitations and 30 invitations: (79 - 54) / (30 - 20) = 25 / 10 = 5/2
Between 30 invitations and 40 invitations: (104 - 79) / (40 - 30) = 25 / 10 = 5/2
The slope is consistent between each pair of points, indicating a linear relationship.
Looking at the choices, the equation that matches the slope 5/2 is:
D. Y = 5/2x + 4