37.2k views
2 votes
Write an equation of the line that is perpendicular to 5x+20y=10 and passes through the point (8,3)

2 Answers

5 votes
Write an equation of the line that is perpendicular to 5x+20y=10 and passes through the point (8,3)
Write an equation of the line that is perpendicular to 5x+20y=10 and passes through-example-1
User Jordan Jambazov
by
7.9k points
0 votes

Answer: The required equation of the line is
y=4x-29.

Step-by-step explanation: We are given to write the equation of the line that is perpendicular to the following line and passes through the point (8, 3).


5x+20y=10~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We know that

the slope-intercept form of a straight line is given by


y=mx+c,

where m is the slope and c is the y-intercept of the line.

From equation (i), we have


5x+20y=10\\\\\Rightarrow 20y=-5x+10\\\\\\\Rightarrow y=-(5)/(20)x+(10)/(20)\\\\\\\Rightarrow y=-(1)/(4)x+(1)/(2).

So,


\textup{slope, }m=-(1)/(4)~~\textup{and}~~\textup{y-intercept, }c=(1)/(2)

Since the product of the slopes of two perpendicular lines is - 1.

Let, m' be the slope of the line perpendicular to line (i).

Then, we must have


m* m'=-1\\\\\\\Rightarrow -(1)/(4)* m'=-1\\\\\Rightarrow m'=4.

Since the line passes through the point (8, 3), so its equation will be


y-3=m'(x-8)\\\\\Rightarrow y-3=4(x-8)\\\\\Rightarrow y=4x-32+3\\\\\Rightarrow y=4x-29.

Thus, the required equation of the line is
y=4x-29.

User Vanlooverenkoen
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories