2. Write an equation in point-slope form to represent the amount charged, C, for m number of miles by the company in Charlotte. (Hint: Go to Desmos and convert the equation you created in #1 to a table. Use a point from the table)
The point-slope equation of a line is given by:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope of the line, \( (x_1, y_1) \) is a point on the line, \(x\) represents the independent variable, and \(y\) represents the dependent variable. In the given context, we need to create an equation that represents the amount charged \(C\) for \(m\) number of miles by a company in Charlotte.
Assuming you have already determined the slope from the first question, and given a specific point from the table after converting the equation to a table in Desmos, let's say that the slope (representing the rate per mile) is \(k\) and one of the points from your table is \( (m_1, C_1) \), where \(m_1\) is a specific number of miles and \(C_1\) is the corresponding charge.
The point-slope form of the equation to represent the amount charged for \(m\) number of miles would be:
\[ C - C_1 = k(m - m_1) \]
where:
- \(C\) is the amount charged for \(m\) miles (in dollars),
- \(k\) is the slope (cost per mile, in dollars per mile),
- \(m_1\) is the number of miles at the specific point from the table,
- \(C_1\) is the amount charged at that number of miles \(m_1\).
Please obtain the actual numerical values for \( k \), \( m_1 \), and \( C_1 \) from your previous work or the Desmos table to complete the equation with actual numbers.