To write the equation of a line in point-slope form, we will use the point-slope formula, which is given by:
[tex]\[ y - y_1 = m (x - x_1) \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope of the line. According to the problem:
- The given point [tex]\((x_1, y_1)\)[/tex] through which the line passes is [tex]\((-6, 8)\)[/tex].
- The given slope [tex]\(m\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].
Now, substitute the values into the point-slope formula:
1. [tex]\(x_1 = -6\)[/tex]
2. [tex]\(y_1 = 8\)[/tex]
3. [tex]\(m = \frac{3}{2}\)[/tex]
The equation of the line in point-slope form becomes:
[tex]\[ y - 8 = \frac{3}{2} (x - -6) \][/tex]
Simplifying the double negative in the expression [tex]\((x - -6)\)[/tex], we get:
[tex]\[ y - 8 = \frac{3}{2} (x + 6) \][/tex]
Therefore, the equation of the line in point-slope form is:
[tex]\[ y - 8 = \frac{3}{2} (x + 6) \][/tex]
This is the point-slope form of the line passing through the point [tex]\((-6, 8)\)[/tex] with a slope of [tex]\(\frac{3}{2}\)[/tex].
