## Question

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

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.