Question
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
A. Y = 5/2x - 4
B. Y = 10/3x - 4
C. Y = 2/5x + 4
D. Y = 5/2x + 4
Answers
GPT 3.5
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.
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.