The cost of producing 330330 stereo speakers is $3245$⁢3245. Producing 800800 stereo speakers would cost $6065$⁢6065.

Step 2 of 3:

Assuming the total cost is a linear function, write an equation for the cost of producing x stereo speakers.

We are tasked with finding a linear equation for the cost of producing $x$ stereo speakers. The given data points are:

- Producing 330 stereo speakers costs \$3245.
- Producing 800 stereo speakers costs \$6065.

### Step 1: Form the equation of a line
A linear cost function has the form:
\[
C(x) = mx + b
\]
where:
- $C(x)$ is the total cost of producing $x$ stereo speakers,
- $m$ is the rate of change (slope), and
- $b$ is the fixed cost (y-intercept).

### Step 2: Calculate the slope ($m$)
The slope $m$ represents the change in cost per unit produced. Using the two points $(330, 3245)$ and $(800, 6065)$, we can find the slope using the formula:
\[
m = \frac{C_2 - C_1}{x_2 - x_1}
\]
Substitute the given values:
\[
m = \frac{6065 - 3245}{800 - 330} = \frac{2820}{470} = 6
\]
So, the slope $m = 6$. This means the cost increases by \$6 for each additional stereo speaker produced.

### Step 3: Find the y-intercept ($b$)
Now that we know $m = 6$, we can use one of the points to find $b$. Using the point $(330, 3245)$ in the equation $C(x) = mx + b$:
\[
3245 = 6(330) + b
\]
\[
3245 = 1980 + b
\]
\[
b = 3245 - 1980 = 1265
\]
Thus, the y-intercept $b = 1265$.

### Final Equation:
The equation for the cost function is:
\[
C(x) = 6x + 1265
\]

This is the equation that describes the cost of producing $x$ stereo speakers.

Would you like any further details or clarification?

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Here are 5 related questions:
1. How would the equation change if the cost per speaker increases?
2. Can you calculate the cost for producing 500 stereo speakers using this equation?
3. What is the fixed cost of production, and how can we interpret it?
4. How would you graph this cost function?
5. If the cost for producing 1000 speakers is known, how can we verify the equation?

**Tip**: Always check your slope calculation when interpreting linear functions, as it represents the rate of change in context.

The cost of producing 330 stereo speakers is $3245. Producing 800 stereo speakers would cost $6065. Assuming the total cost is a linear function, write an equation for the cost of producing x stereo speakers.

Learn how to write a linear equation for the cost of producing stereo speakers based on two data points: 330 speakers costing $3245 and 800 speakers costing $6065. This problem covers key algebra concepts like slope-intercept form and cost functions, suitable for Grades 8-10.

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