the slope - intercept form of the equation of a line that passes through point (-3, 8) is $y = -\frac{2}{3}x…

the slope - intercept form of the equation of a line that passes through point (-3, 8) is $y = -\frac{2}{3}x + 6$. what is the point - slope form of the equation for this line?\n$y - 3=-\frac{2}{3}(x + 8)$\n$y + 3=-\frac{2}{3}(x - 8)$\n$y + 8=-\frac{2}{3}(x - 3)$\n$y - 8=-\frac{2}{3}(x + 3)$

the slope - intercept form of the equation of a line that passes through point (-3, 8) is $y = -\frac{2}{3}x + 6$. what is the point - slope form of the equation for this line?\n$y - 3=-\frac{2}{3}(x + 8)$\n$y + 3=-\frac{2}{3}(x - 8)$\n$y + 8=-\frac{2}{3}(x - 3)$\n$y - 8=-\frac{2}{3}(x + 3)$

Answer

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify values

Given the line passes through the point $(-3,8)$ and from the slope - intercept form $y =-\frac{2}{3}x + 6$, the slope $m=-\frac{2}{3}$, $x_1=-3$ and $y_1 = 8$.

Step3: Substitute values

Substitute $x_1=-3$, $y_1 = 8$ and $m =-\frac{2}{3}$ into the point - slope form: $y - 8=-\frac{2}{3}(x-(-3))$, which simplifies to $y - 8=-\frac{2}{3}(x + 3)$.

Answer:

$y - 8=-\frac{2}{3}(x + 3)$