Question

Write the equation of the line that is perpendicular to y = -2/3 x +2 and goes through the point (-1, 4). Make sure your final answer is in slope-intercept form

Answer 1

Given:

The equation of a line is

$y=-\dfrac{2}{3}x+2$          ...(i)

The perpendicular line passes through the point (-1,4).

To find:

The equation of the perpendicular line.

Solution:

The slope intercept form of a line is:

$y=mx+b$            ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

$m=-\dfrac{2}{3}$

Product of slopes of two perpendicular lines is -1.

Let the slope of perpendicular line is $m_1$.

$m\times m_1=-1$

$-\dfrac{2}{3}\times m_1=-1$

$m_1=\dfrac{3}{2}$

The slope of the perpendicular line is $m_1=\dfrac{3}{2}$ and it passes through the point (-1,4). So, the equation of the line is:

$y-y_1=m_1(x-x_1)$

$y-4=\dfrac{3}{2}(x-(-1))$

$y-4=\dfrac{3}{2}(x+1)$

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

Add 4 on both sides.

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

$y=\dfrac{3}{2}x+\dfrac{3+8}{2}$

$y=\dfrac{3}{2}x+\dfrac{11}{2}$

Therefore, the equation of required line is $y=\dfrac{3}{2}x+\dfrac{11}{2}$.