Question

Consider the line {3} x+1 " alt=" y=\frac{2}{3} x+1 " align="absmiddle" class="latex-formula">.
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 5)

Find the equation of the line that is parallel to this line and passes through the point (-4, -5)

Equation of perpendicular:

Equation of parallel line:

Answer 1

we are given equation of line

$y=\frac{2}{3} x+1$

Equation of perpendicular line:

Firstly , we will find slope of line

$y=\frac{2}{3} x+1$

we can compare it with

y=mx+b

we get

$m=\frac{2}{3}$

we know that

slope of perpendicular line will be -1/m

so, slope is

$\frac{-3}{2}$

It passes through point (-4,5)

so, we can use point slope form of line

$y-5=-\frac{3}{2}(x+4)$

we get

$y=-\frac{3}{2}x-1$..........Answer

Equation of parallel line:

Firstly , we will find slope of line

$y=\frac{2}{3} x+1$

we can compare it with

y=mx+b

we get

$m=\frac{2}{3}$

we know that

slope of parallel line always equal

so, slope is

$\frac{2}{3}$

It passes through point (-4,-5)

so, we can use point slope form of line

$y+5=\frac{2}{3}(x+4)$

we get

$y=\frac{2}{3}x-\frac{7}{3}$............Answer