you produce 2000 brownies in a month you have a monthly cost of $1500. when you produce 4000 brownies your monthly cost is $2000. assume that each brownie has a constant amount answer the folloing questons : a. write down a linar equation that gives the cost amout , the products, and the dollar amount
so you have 2 ordered pairs of the type
(brownies, cost) , (2000,1500) , (4000, 2000)
slope = (2000-1500)/(4000-2000) = 500/2000 = 1/4
using the 2nd point, ...
cost - 2000 = (1/4)(brownies - 4000)
4 C - 8000 = B - 4000
B - 4C = -4000
(checking if 1st point satisfies ...
LS = 2000 - 4(1500)
= -4000 = RS, YUPP )
variations:
B = 4C - 4000
-4C = -B - 4000
C = (1/4)B + 1000
To find a linear equation that relates the cost amount, number of products, and the dollar amount, we need to determine the equation of a line in the form y = mx + b, where y represents the cost amount, x represents the number of products, and b represents the y-intercept (the cost amount when x = 0).
Let's use the given data points to find the equation:
1. When you produce 2000 brownies (x = 2000), the monthly cost is $1500 (y = 1500).
2. When you produce 4000 brownies (x = 4000), the monthly cost is $2000 (y = 2000).
We can use these two points to find the slope (m) of the line:
m = (y2 - y1) / (x2 - x1)
= (2000 - 1500) / (4000 - 2000)
= 500 / 2000
= 0.25
Now that we have the slope, we can substitute one of the given points (x, y) into the equation to solve for b:
1500 = 0.25 * 2000 + b
1500 = 500 + b
b = 1500 - 500
b = 1000
Therefore, the linear equation that relates the cost amount (y), number of products (x), and dollar amount is:
y = 0.25x + 1000