Question

Find an equation for the line that passes through the points (1,-2) and (-5,6).

Answer 1

Consider a line passing throug the following points:

`\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}`

Any equation passing through these two points can be expressed in the slope intercept form:

`\begin{gathered} y=ax+b \\ a=(y_2-y_1)/(x_2-x_1) \\ b=y_1-ax_1=y_2-ax_2 \end{gathered}`

Then, for a line passing through the points (1,-2) and (-5,6), we have:

`\begin{gathered} a=((-2)-6)/(1-(-5))=-(8)/(6)=-(4)/(3) \\ b=-2-(-(4)/(3))\cdot1=-(2)/(3) \\ \therefore y=-(4)/(3)x-(2)/(3) \end{gathered}`