Question

Write the equation of the line that is perpendicular to 3x+2y=8 and goes through the point (-5,2)

Answer 1

Answer:

$\displaystyle y=\frac{2}{3}(x+5)+2$

Step-by-step explanation:

We need to find the equation of the line perpendicular to the line 3x+2y=8 and passes through (-5,2).

The given line can be expressed as:

$\displaystyle y=-\frac{3}{2}x+4$

We can see the slope of this line is m1=-3/2.

The slopes of two perpendicular lines, say m1 and m2, meet the condition:

$m_1.m_2=-1$

Solving for m2:

$\displaystyle m_2=-\frac{1}{m_1}$

$\displaystyle m_2=-\frac{1}{-\frac{3}{2}}$

$\displaystyle m_2=\frac{2}{3}$

Now we know the slope of the new line, we use the slope-point form of the line:

$y=m(x-h)+k$

Where m is the slope and (h,k) is the point. Using the provided point (-5,2):

$\boxed{\displaystyle y=\frac{2}{3}(x+5)+2}$