Kites Purchased| Total Cost for Kites-R-Fun
0| $8
1| $12
4| $48
7| $84
10| $120
Write an equation for the total cost, y, in terms of the number of kites purchased x:
The data points suggest a linear relationship between the number of kites purchased (x) and the total cost (y). We can find the equation for this relationship by finding the slope of the line that passes through two of the points and then using the point-slope form of a linear equation.
Let's choose the points (0, $8) and (10, $120) to find the slope:
slope = change in y / change in x
= ($120 - $8) / (10 - 0)
= $112 / 10
= $11.20
Using the point-slope form of a linear equation, we can write:
y - y1 = m(x - x1)
Taking (0, $8) as (x1, y1) and the slope we found as m:
y - 8 = 11.20(x - 0)
y - 8 = 11.20x
y = 11.20x + 8
Therefore, the equation for the total cost, y, in terms of the number of kites purchased x is:
y = 11.20x + 8
Are you sure that’s correct?
Apologies for the mistake. Let's recalculate the equation using the correct data points.
Using the points (1, $12) and (10, $120):
slope = change in y / change in x
= ($120 - $12) / (10 - 1)
= $108 / 9
= $12
Using the point-slope form of a linear equation:
y - y1 = m(x - x1)
Taking (1, $12) as (x1, y1) and the slope we found as m:
y - 12 = 12(x - 1)
y - 12 = 12x - 12
y = 12x
Therefore, the correct equation for the total cost, y, in terms of the number of kites purchased x is:
y = 12x