Question

What is an equation of the line that passes through the points (-3,-5) and (-5, -3)? Put your answer in fully reduced form.

Answer 1

Express the general equation of a line passing through two points (x1,y1) and (x2,y2).

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

Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,

`\begin{gathered} y+5=(-3+5)/(-5+3)(x+3) \\ y+5=(2)/(-2)(x+3) \\ y+5=-x-3 \end{gathered}`

Further simplifying gives,

`y=-x-8`

Therefore, the equation of the line is y=-x-8.