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.