A surf instructor has an initial fee of $12 and charges $8 per hour for lessons.

Question

Write a linear equation that represents the total cost of surf lessons after a certain number of hours.

1.y-intercept = (0, 12), point = (x, y)

2.m = 8

3. 8 =
y − 12
x − 0
→ 8 =
y − 12
x

4.Solve for y:

Answer 1

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:

1. The initial fee (y-intercept) is $12, which represents the starting cost before any hours of lessons are taken.
2. 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:

1. 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:

\[ y = 8x + 12 \]