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Question

Find the equation of the line that passes through point `(-3,5)` and is perpendicular to the line `4x+3y=6`.

Answer

Two lines `y=m_1x+b_1` and `y=m_2 x+b_2` are perpendicular if `m_1=-1/m_2`.

So, rewrite the line in a slope-intercept form: `4x+3y=6` becomes `y=-4/3 x+2`.

Thus, `m_1=-4/3` and `m_2=-1/m_1=-1/(-4/3)=3/4`.

Equation of the second line is, therefore, `y=3/4 x+b_2`.

To find `b_2` use the fact that line passes through the point `(-3,5)`:

`5=3/4(-3)+b_2`

From this equation `b_2=5+9/4=29/4`.

Finally, equation of the line is `y=3/4 x+29/4`.

Answer: `y=3/4 x+29/4`.