Question

Find the equation of the line that passes through the points: (2, 2) and (3, 4) y = 2x + 2 y = -2x - 2y = -2x + 2 y = 2x - 2

Answer 1

Solution

To find the equation of the line that passes through the points (2, 2) and (3, 4)

we use the formula

$\frac{y_-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Here,

$\begin{gathered} x_1=2 \\ \\ y_1=2 \\ \\ x_2=3 \\ \\ y_2=4 \end{gathered}$

$\begin{gathered} \frac{y-2}{x-2}=\frac{4-2}{3-2} \\ \\ \frac{y-2}{x-2}=\frac{2}{1} \\ \\ y-2=2\left(x-2\right) \\ \\ y-2=2x-4 \\ \\ y=2x-4+2 \\ \\ y=2x-2 \end{gathered}$

Hence, the equation is y = 2x - 2