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A surf instructor has an initial fee of [tex]$\$[/tex]12[tex]$ and charges $[/tex]\[tex]$8$[/tex] per hour for lessons.

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

1. [tex]$y$[/tex]-intercept [tex]$=(0,12)$[/tex], point [tex]$=(x, y)$[/tex]
2. [tex]$m=8$[/tex]
3. [tex]$8=\frac{y-12}{x}$[/tex]
4. Solve for [tex]$y$[/tex] :
[tex]\[ y = 8x + 12 \][/tex]

Sagot :

GinnyAnswer
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]
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