Given:
[tex]\begin{gathered} \text{ Equation of the line that is perpendicular to }y=-\frac{3}{4}x+1\text{ and contains} \\ \text{the point }(9,12). \end{gathered}[/tex]
Required:
Find the equation of the line.
Explanation:
Condition for lines to be perpendicular:
[tex]\begin{gathered} y=mx+c \\ y=-\frac{1}{m}x+c \end{gathered}[/tex][tex]\begin{gathered} \text{ So, line is perpendicular to }y=-\frac{3}{4}x+1 \\ \text{ That is }y=\frac{4}{3}x+c \\ \text{ and contains the points }(9,12) \\ 12=\frac{4}{3}\times9+c \\ c=0 \\ \text{ The line is }y=\frac{4}{3}x+0 \end{gathered}[/tex]
Answer:
[tex]\text{ The line is }y=\frac{4}{3}x+0[/tex]
