Let's work through the problem step-by-step to identify which equation correctly represents Zada's pay, [tex]\( y \)[/tex], when she works [tex]\( x \)[/tex] hours in point-slope form.
1. Identify Given Values:
- Hourly rate, [tex]\( m = 12 \)[/tex] dollars per hour.
- Total earnings when working 4 hours, [tex]\( y = 68 \)[/tex] dollars.
- Number of hours worked, [tex]\( x = 4 \)[/tex] hours.
2. Determine the point-slope form of the equation:
The point-slope form of a linear equation is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where:
- [tex]\( (x_1, y_1) \)[/tex] is a specific point on the line.
- [tex]\( m \)[/tex] is the slope of the line (hourly rate in this case).
3. Substitute known values:
In this scenario, the specific point is [tex]\( (4, 68) \)[/tex]:
- [tex]\( x_1 = 4 \)[/tex]
- [tex]\( y_1 = 68 \)[/tex]
- [tex]\( m = 12 \)[/tex]
Substituting these values into the point-slope form equation, we get:
[tex]\[
y - 68 = 12(x - 4)
\][/tex]
4. Compare the equations:
- [tex]\( y + 68 = 12(x + 4) \)[/tex]
- [tex]\( y + 4 = 12(x + 68) \)[/tex]
- [tex]\( y - 68 = 12(x - 4) \)[/tex]
- [tex]\( y - 4 = 12(x - 68) \)[/tex]
The equation we derived is:
[tex]\[
y - 68 = 12(x - 4)
\][/tex]
This matches the third option. Therefore, the correct equation in point-slope form that represents Zada's pay, [tex]\( y \)[/tex], when she works [tex]\( x \)[/tex] hours is:
[tex]\[ y - 68 = 12(x - 4) \][/tex]
