Sure! Let's break down the steps to write a linear equation that represents the total cost of surf lessons after a certain number of hours.
1. Identifying the y-intercept and the slope:
- The y-intercept is given as (0, 12). This means when the number of hours (x) is 0, the total cost (y) is $12.
- The slope (m), which represents the rate at which the cost increases per hour, is given as 8.
2. Using the slope-intercept form of a linear equation:
- The general form of a linear equation in slope-intercept form is [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.
3. Given values:
- Slope [tex]\( m = 8 \)[/tex]
- y-intercept [tex]\( c = 12 \)[/tex]
4. Substituting the given values into the slope-intercept form:
- Replace [tex]\( m \)[/tex] with 8 and [tex]\( c \)[/tex] with 12 in the equation [tex]\( y = mx + c \)[/tex].
5. Formulating the equation:
- Substituting these values, we get [tex]\( y = 8x + 12 \)[/tex].
Thus, the linear equation that represents the total cost [tex]\( y \)[/tex] of surf lessons after [tex]\( x \)[/tex] hours is:
[tex]\[ y = 8x + 12 \][/tex]
