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=(y_2-y_1)/(x_2-x_1)`

Fisrt line:

In this case the slope is

`\begin{gathered} m=(-3-1)/(0-3) \\ =(-4)/(-3) \\ =(4)/(3) \end{gathered}`

The the equation is

`y-1=(4)/(3)(x-3)`

Second line:

In this case the slope is

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

Then the equation is

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