Question

Find the equation of the line perpendicular to -9x+4y=8 that contains the point (9,7)

Answer 1

`\[y=-(4)/(9)x+11\]`

Explanation:

Equation of the given line is
`\[-9x+4y=8\]`

Slope of the line =
`\[(9)/(4)\]`

Slope of the perpendicular line =
`\[-(4)/(9)\]`

Equation of the line perpendicular to the given line is
`\[y=mx+c\]`

`\[y=-(4)/(9)x+c\]`

But this line passes through (9,7)

Substituting the values in the equation:

`\[7=-4+c\]`

=>
`\[c=7+4=11\]`

So the overall equation of the parallel line is given by
`\[y=-(4)/(9)x+11\]`