Question

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

​(3​,−2​) and ​(5​,2​)

Answer 1

The equation of line passing through two points $(x_1,y_1)\ \text{and}\ (x_2,y_2)$ is:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

Here two points are ​(3​,−2​) and ​(5​,2​).

Let $(x_1,y_1)=(3,-2), (x_2,y_2)=(5,2)$

Thus, equation of line is

$y+2=\frac{2+2}{5-3} (x-3)\\ y+2=2x-6\\ y=2x-8\\ f(x)=2x-8$