To convert the slope-intercept form [tex]\( y = -\frac{2}{3}x + 6 \)[/tex] into point-slope form, we will utilize the point [tex]\((-3, 8)\)[/tex] through which the line passes.
The point-slope form of a line equation is generally given by:
[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 slope [tex]\( m = -\frac{2}{3} \)[/tex]
- The point [tex]\((x_1, y_1) = (-3, 8)\)[/tex]
Substitute these values into the point-slope form equation:
[tex]\[ y - 8 = -\frac{2}{3}(x + 3) \][/tex]
Thus, the point-slope form of the equation of the line that passes through [tex]\((-3, 8)\)[/tex] with the slope of [tex]\(-\frac{2}{3}\)[/tex] is:
[tex]\[ y - 8 = -\frac{2}{3}(x + 3) \][/tex]
Therefore, the correct answer is:
[tex]\[ y - 8 = -\frac{2}{3}(x + 3) \][/tex]
Hence, the correct multiple-choice option is:
[tex]\[ y - 8 = -\frac{2}{3}(x + 3) \][/tex]
