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

Sagot :

Consider a line passing throug the following points:

[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]

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

[tex]\begin{gathered} y=ax+b \\ a=\frac{y_2-y_1}{x_2-x_1} \\ b=y_1-ax_1=y_2-ax_2 \end{gathered}[/tex]

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

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

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