Answered

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In what form is the following linear equation written?

[tex]\[ y - 3 = \frac{2}{3}(x - 1) \][/tex]

A. Slope-intercept
B. Rise-run
C. Standard
D. Point-slope

Sagot :

GinnyAnswer
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
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