Question

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

Answer 1

`\displaystyle y=(2)/(3)(x+5)+2`

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=-(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=-(1)/(m_1)`

`\displaystyle m_2=-(1)/(-(3)/(2))`

`\displaystyle m_2=(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=(2)/(3)(x+5)+2}`