# Find an equation of the line containing the given pair of points. (3,2) and (9,7)

## Question:

Find an equation of the line containing the given pair of points.

## 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 point-slope form: {eq}y-y_1=m(x-x_1) {/eq}.

The given two points on the line are:

$$(x_1,y_1) = (3,2) \\ (x_2,y_2)= (9, 7)$$

The slope of the line is found using:

\begin{align} m&= \dfrac{y_2-y_1}{x_2-x_1} \\ &= \dfrac{7-2}{9-3} \\ &= \dfrac{5}{6} \end{align}

The equation of the line is found using:

$$y-y_1=m(x-x_1) \\ y-2=\dfrac{5}{6} (x-3) \\ y-2=\dfrac{5}{6}x - \dfrac{5}{2} \\ \text{Adding 2 on both sides} , \\ y= \dfrac{5}{6}x - \dfrac{5}{2}+2 \\ \boxed{\mathbf{y=\dfrac{5}{6}x - \dfrac{1}{2}}}$$