Linear Equations - Forms of a Line 3

Geometry Level 1

What is the equation of a line that passes through two points ( − 2 , − 2 ) (-2,-2) and ( 4 , 1 ) (4, 1) ?

y = 1 2 x − 1 y = \frac12 x - 1 y = x − 1 y = x - 1 y = 1 2 x − 2 y = \frac12 x - 2 y = 1 2 x + 1 y = \frac12 x+ 1

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1 solution

Brilliant Mathematics Staff
Aug 1, 2020

Use point-point form of a line y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) to find the equation.

Let ( x 1 , y 1 ) = ( − 2 , − 2 ) (x_1, y_1) = (-2, -2) and ( x 2 , y 2 ) = ( 4 , 1 ) (x_2, y_2) = (4, 1) . Then we have

y − ( − 2 ) = 1 − ( − 2 ) 4 − ( − 2 ) ( x − ( − 2 ) ) y + 2 = 1 2 ( x + 2 ) y = 1 2 x − 1. \begin{aligned} y - (-2) &= \frac{1 - (-2)}{4 - (-2)}(x - (-2)) \\ y + 2 &= \frac{1}{2} (x+2) \\ y &= \frac12 x -1. \end{aligned}

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