Mathematics: Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y = 4/3x. show your work plz.

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Find the equation of a line that passes through

yessy73

09.06.2020

Required Equation of line is 4y + 3x = 20

Step-by-step explanation:

Given: Passing through point of a line ( 4 , 2 )

Equation of line : $y=\frac{4}{3}x$

We have to find an equation of line which is perpendicular to given line and passes through given point.

First we find slope of given line by comparing it with Slope-intercept form of line, y = mx + c

we get, $Slope=\frac{4}{3}$

let slope of required line be m.

we know that Product of the perpendicular lines equals to -1.

$\implies m\times\frac{4}{3}=-1$

$m=-1\times\frac{3}{4}$

$m=\frac{-3}{4}$

So, Using Slope and point form we find equation of required line,

y-y_1=m(x-x_1)

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

$4\times(y-2)=-3(x-4)$

4y-8=-3x+12

4y+3x=8+12

4y+3x=20

Therefore, Required Equation of line is 4y + 3x = 20

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