A line passes through the point [tex][tex]$(-9,6)$[/tex][/tex] and has a slope of [tex]\frac{2}{3}[/tex].

Write an equation in point-slope form for this line.



Answer :

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]