(b)  Find a linear cost equation in slope-intercept form that will represent the cost of mining x ounces of silver.  (An answer to this part in the proper format is

C=46x-300

To find a linear cost equation in slope-intercept form that represents the cost of mining $ x $ ounces of silver, the general format is:

\[
C = mx + b
\]

Where:
- $ C $ is the total cost of mining.
- $ x $ is the number of ounces of silver mined.
- $ m $ is the slope of the line, which represents the cost per ounce of silver.
- $ b $ is the y-intercept, which represents the fixed or starting cost (even if no silver is mined).

In the given example:

\[
C = 46x - 300
\]

Here:
- The slope $ m = 46 $ indicates that the cost of mining each additional ounce of silver is \$46.
- The y-intercept $ b = -300 $ suggests that there is an initial savings or subsidy of \$300. This could imply that the mining operation starts with a \$300 credit, or some other kind of negative initial cost.

### Summary:

\[
C = 46x - 300
\]
This equation represents the total cost of mining $ x $ ounces of silver, where each ounce costs \$46 to mine, but there's an initial \$300 reduction in cost.

Would you like further explanation or have any questions?

### Related Questions:
1. What does the slope of a linear equation represent in practical terms?
2. How would the equation change if there was no initial cost reduction?
3. How can you determine the break-even point from a linear cost equation?
4. What happens if the cost per ounce increases to \$50? How would that affect the equation?
5. How can we interpret a positive intercept in a cost equation?

### Tip:
Always check if the intercept (fixed cost) makes sense in the context of the problem, as it can sometimes represent subsidies or initial investments.

Find a linear cost equation in slope-intercept form that will represent the cost of mining x ounces of silver.

Discover how to form a linear cost equation in slope-intercept form for mining silver. This example uses the equation C = 46x - 300, where each ounce of silver costs $46 and an initial $300 reduction is applied. Suitable for students in Grades 8-10.

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