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The slope-intercept form of the equation of a line that passes through point [tex]$(-3,8)$[/tex] is [tex]y = -\frac{2}{3} x + 6[/tex]. What is the point-slope form of the equation for this line?
A. [tex]y - 3 = -\frac{2}{3} (x + 8)[/tex] B. [tex]y + 3 = \frac{2}{3} (x - 8)[/tex] C. [tex]y + 8 = \frac{2}{3} (x - 3)[/tex] D. [tex]y - 8 = -\frac{2}{3} (x + 3)[/tex]
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:
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