To write the equation of a line in point-slope form, we use the formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope of the line.
Given:
- The point [tex]\((-9, 6)\)[/tex] (i.e., [tex]\(x_1 = -9\)[/tex] and [tex]\(y_1 = 6\)[/tex])
- The slope [tex]\(m = \frac{2}{3}\)[/tex]
We substitute the values of [tex]\(x_1\)[/tex], [tex]\(y_1\)[/tex], and [tex]\(m\)[/tex] into the point-slope form equation:
[tex]\[ y - 6 = \frac{2}{3}(x - (-9)) \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ y - 6 = \frac{2}{3}(x + 9) \][/tex]
To express the slope as a decimal for a more precise answer, [tex]\(\frac{2}{3}\)[/tex] is approximately 0.6666666666666666.
Thus, the equation in point-slope form is:
[tex]\[ y - 6 = 0.6666666666666666(x + 9) \][/tex]
