Use the given conditions to write an equation for the line in point-slope form.
Passing through $(-6,-5)$ and $(-3,-7)$
\[
y-5=-
\]
(A) $(x-6)$ or $y-7=-$
\[
\begin{array}{l}
(x-3) \\
y+5=-
\end{array}
\]
(B) $(x+6)$ or $y+7=$
(C) $(x+3)$ or $y+7=-$
\[
\begin{array}{l}
(x+6) \\
y+5=
\end{array}
\]
(D) $x-6$ or $y+7=-$
\[
\frac{2}{3}
\]
$\frac{2}{3}$

Answer

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Answer

$\boxed{y + 5 = -\frac{2}{3}(x + 6)}$

Steps

Step 1 ：Find the slope of the line passing through the given points: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - (-5)}{-3 - (-6)} = \frac{-2}{3}$

Step 2 ：Use the point-slope form to write the equation of the line: $y - y_1 = m(x - x_1)$

Step 3 ：Substitute the slope and one of the points, for example, $(-6, -5)$: $y - (-5) = -\frac{2}{3}(x - (-6))$

Step 4 ：$\boxed{y + 5 = -\frac{2}{3}(x + 6)}$