Problem

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 $y+7=-$ \[ \frac{2}{3} \] $\frac{2}{3}$

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/16076/

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