Find an equation of the line that contains the following pair of points. (-2,-3) and (-6,-9)

Question:

Find an equation of the line that contains the following pair of points.

{eq}\left ( -2,-3 \right ) {/eq} and {eq}\left ( -6,-9 \right ) {/eq}

Equation of a Line:

To find the equation of a line through two given points {eq}(x_1,y_1) {/eq} and {eq}(x_2, y_2) {/eq}:

(i) Find its slope using: {eq}m= \dfrac{y_2-y_1}{x_2-x_1} {/eq}.

(ii) The equation of the line is found using: {eq}y-y_1=m(x-x_1) {/eq}.

The points on the line are:

$$(x_1,y_1)=(-2, -3)\\ (x_2, y_2)= (-6,-9)$$

The slope of the line is found using:

\begin{align} m&= \dfrac{y_2-y_1}{x_2-x_1} \\ &= \dfrac{-9-(-3)}{-6-(-2)} \\ &= \dfrac{-6}{-4} \\ &= \dfrac{3}{2} \end{align}

The equation of the line is found using:

$$y-y_1=m(x-x_1)\\ y-(-3)= \dfrac{3}{2} (x-(-2)) \\ y+3= \dfrac{3}{2} (x+2) \\ y+3= \dfrac{3}{2} x + 3 \\ \text{Subtracting 3 from both sides}, \\ \boxed{\mathbf{y=\dfrac{3}{2}x}}$$.