To determine the form in which the equation [tex]\( y - 3 = \frac{2}{3}(x - 1) \)[/tex] is written, let's analyze it step-by-step.
1. Identify the structure of the equation:
The equation [tex]\( y - 3 = \frac{2}{3}(x - 1) \)[/tex] appears to be in the form [tex]\( y - y_1 = m(x - x_1) \)[/tex].
2. Recognize the variables and constants:
- [tex]\( y_1 \)[/tex] represents the y-coordinate of a specific point on the line.
- [tex]\( x_1 \)[/tex] represents the x-coordinate of that point.
- [tex]\( m \)[/tex] is the slope of the line.
3. Compare the given equation to the general form:
Given equation: [tex]\( y - 3 = \frac{2}{3}(x - 1) \)[/tex]
General form: [tex]\( y - y_1 = m(x - x_1) \)[/tex]
Here, it is clear that:
- [tex]\( y_1 = 3 \)[/tex]
- [tex]\( x_1 = 1 \)[/tex]
- [tex]\( m = \frac{2}{3} \)[/tex]
4. Determine the form of the equation:
The point-slope form of a linear equation is given by [tex]\( y - y_1 = m(x - x_1) \)[/tex], which matches the structure of the provided equation.
Therefore, the equation [tex]\( y - 3 = \frac{2}{3}(x - 1) \)[/tex] is written in the point-slope form.
So, the answer is:
D. Point-slope
