Question

Find an equation of the line passing through the given points. Use function notation to write the equation.

​(−2​,−2​) and ​(−4​,−3​)

Answer 1

The equation of a straight line passing through two points $A(x_1,y_1) \text{~and~} B(x_2,y_2)$ is

$\dfrac{y - y_1}{y_2 - y_1} = \dfrac{x - x_1}{x_2 - x_1}$.

Here, $A = (-2,-2), B = (-4,-3)$. Hence

$\begin{aligned} \dfrac{y + 2}{-3+2}&= \dfrac{x + 2}{-4+2}\\ 2(y+2)&=x+2\\ 2y+4&=x+2\\ 2y&= x - 2\\ y& = \dfrac{x-2}{2} \end{aligned}$

The function notation of the straight line is $f(x) = \dfrac{x-2}{2}.$