Sally's school donated an initial amount for a fundraising event to be organised. Sally was in charge of collecting more money for the event over the course of 10 days. The table below shows the total amount collected at the end of a given number of days. Number of Days, x Amount Collected, y ($) 2 315 4 380 6 445 8 510 Which equation describes the relationship between the amount of money collected and the number of days the fundraiser has been in progress? A. B. C. D.
Using the given information, we can graph the points (2, 315), (4, 380), (6, 445), and (8, 510). By looking at the graph, we can see that the relationship between the amount of money collected and the number of days is linear.
To find the equation of the line, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is one of the given points, and m is the slope of the line.
Using the slope formula, m = (y2 - y1)/(x2 - x1), we can find the slope from the first two points: m = (380 - 315)/(4 - 2) = 65/2.
Using the point-slope form with the point (2, 315) and the slope m = 65/2, we have:
y - 315 = (65/2)(x - 2)
Simplifying, we get:
y - 315 = (65/2)x - 65
Adding 315 to both sides:
y = (65/2)x - 65 + 315
Simplifying further, we have:
y = (65/2)x + 250
Therefore, the equation that describes the relationship between the amount of money collected and the number of days the fundraiser has been in progress is:
y = (65/2)x + 250
So the answer is C.