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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.

{eq}(3,2) \quad {/eq}and{eq}\quad (9,7) {/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 point-slope form: {eq}y-y_1=m(x-x_1) {/eq}.

Answer and Explanation:

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:

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


Learn more about this topic:

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Calculating the Slope of a Line: Point-Slope Form, Slope-Intercept Form & More

from Geometry: High School

Chapter 12 / Lesson 5
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