Question

A line that passes through (3, 1) and (0, -3) A line that passes through (-1,-5) and (2, 4)

Answer 1

The equation of a line is given by

$y-y_1=m(x-x_1)$

where m is the slope and (x1,y1) is a point on the line.

The slope is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

Fisrt line:

In this case the slope is

$\begin{gathered} m=\frac{-3-1}{0-3} \\ =\frac{-4}{-3} \\ =\frac{4}{3} \end{gathered}$

The the equation is

$y-1=\frac{4}{3}(x-3)$

Second line:

In this case the slope is

$\begin{gathered} m=\frac{4-(-5)}{2-(-1)} \\ =\frac{4+5}{2+1} \\ =\frac{9}{3} \\ =3 \end{gathered}$

Then the equation is

$\begin{gathered} y-(-5)=9(x-(-1)) \\ y+5=9(x+1) \end{gathered}$