Given: Two points below:
[tex]\begin{gathered} (7,2) \\ (-2,-5) \end{gathered}[/tex]To Determine: The equation of the line passing through the given line
The formula for finding the equation of the line passing through two given points is
[tex]\begin{gathered} (x_1,y_1);(x_2,y_2) \\ \text{equation formula} \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Use the formula to find the equation of the given points as shown below:
[tex]\begin{gathered} (7,2);(-2,-5) \\ x_1=7;y_1=2 \\ x_2=-2;y_2=-5 \\ By\text{ substitution into the formula} \\ \frac{y-2}{x-7}=\frac{-5-2}{-2-7} \end{gathered}[/tex][tex]\begin{gathered} \frac{y-2}{x-7}=\frac{-7}{-9} \\ \frac{y-2}{x-7}=\frac{7}{9} \\ \text{cross}-\text{multiply} \\ 9(y-2)=7(x-7) \end{gathered}[/tex][tex]\begin{gathered} 9y-18=7x-49 \\ 9y-7x=-49+18 \\ 9y-7x=-31 \end{gathered}[/tex]Hence, the equation of the line passing through the points (7,2) and (-2,-5) is
9y-7x=-31
