To create a linear equation that represents the total cost of surf lessons after a certain number of hours, we can follow the information you provided:
- The initial fee (y-intercept) is $12, which represents the starting cost before any hours of lessons are taken.
- The charge per hour (slope, m) is $8.
We can denote:
- \(y\) as the total cost.
- \(x\) as the number of hours of lessons.
The general form of the linear equation based on the slope-intercept form \(y = mx + b\) is:
\[ y = mx + b \]
Substituting in the values we have:
- \(m = 8\) (the charge per hour)
- \(b = 12\) (the initial fee)
Thus, the equation becomes:
\[ y = 8x + 12 \]
Solving for \(y\):
This equation is already solved for \(y\). However, if we want to rearrange it to isolate \(y\), we can express it as follows:
-
Start with the equation:
\[ y = 8x + 12 \]
This indicates that for every hour of lessons (represented by \(x\)), the total cost (represented by \(y\)) increases by $8, starting from a base cost of $12.
In summary, the linear equation representing the total cost of surf lessons after \(x\) hours is:
\[ y = 8x + 12 \]