a company finds it can produce 15 heaters for $4300, while producing 20 heaters costs $5500. Express y, as a linear function of the number of heaters, y. Determine the cost to produce 30 heaters.
y = _________
Cost to produce 30 heaters $_________
Help I'm not sure how to solve this problem. Thank you
y=mx+b
4300=m*15+b
5500=m*20+b
subtract the first from the second
1200=5m
m= you solve it. THen put it in either equation, and solve for b.
Thank you so much. I can't believe it was so simple..:):)
To determine the linear function representing the cost, y, as a function of the number of heaters, we can use the two given data points:
1. The cost to produce 15 heaters is $4300.
2. The cost to produce 20 heaters is $5500.
Let's calculate the slope of the linear function using these data points. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (x1, y1) = (15, 4300) and (x2, y2) = (20, 5500):
m = (5500 - 4300) / (20 - 15)
m = 1200 / 5
m = 240
So, the slope of the linear function is 240.
Now, let's find the y-intercept (b). We can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using (x, y) = (15, 4300):
y - 4300 = 240(x - 15)
y - 4300 = 240x - 3600
y = 240x - 3600 + 4300
y = 240x + 700
Now, we have the linear function representing the cost, y, as a function of the number of heaters, x.
Next, let's determine the cost to produce 30 heaters by substituting x = 30 into the linear function:
y = 240(30) + 700
y = 7200 + 700
y = 7900
So, the cost to produce 30 heaters is $7900.
To summarize:
y = 240x + 700
Cost to produce 30 heaters = $7900
To express y, the cost, as a linear function of the number of heaters, we can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept.
Let's find the slope first:
Slope (m) = (change in y) / (change in x)
In this case, the change in y is the difference in cost, and the change in x is the difference in the number of heaters produced. So, we have:
Slope (m) = (5500 - 4300) / (20 - 15)
= 1200 / 5
= 240
Now let's find the y-intercept (b):
We can use either of the given data points (15 heaters, $4300) or (20 heaters, $5500).
Using (15 heaters, $4300):
y = mx + b
4300 = 240(15) + b
4300 = 3600 + b
b = 4300 - 3600
b = 700
Now we have the equation for the cost of production (y):
y = 240x + 700
To determine the cost to produce 30 heaters, substitute x = 30 into the equation:
y = 240(30) + 700
y = 7200 + 700
y = $7900
So, y = $7900 is the cost to produce 30 heaters.