Given
The line x+2y=9.
To find:
The equation of the line perpendicular to x+2y=9, and passing throught he point (4,-7).
Explanation:
It is given that,
The line x+2y=9.
Then,
The line perpendicular to x+2y=9 is,
[tex]2x-y=k\text{ \_\_\_\_\_\lparen1\rparen}[/tex]
Since it passes through (4,-7).
Then,
[tex]\begin{gathered} (1)\Rightarrow2(4)-(-7)=k \\ \Rightarrow8+7=k \\ \Rightarrow k=15 \end{gathered}[/tex]
Hence, the equation of the required line is 2x-y=15.
Also, the equation of the line in slope intercept form is, y = 2x-15.
