Find a standard form equation for the line perpendicular to 3x-2y+5=0 and with the same y-intercept as 3x-y+18=0

ajakanvao

ajakanvao

Answered question

2022-11-06

Find a standard form equation for the line perpendicular to 3x-2y+5=0 and with the same y-intercept as 3x-y+18=0

Answer & Explanation

dilettato5t1

dilettato5t1

Beginner2022-11-07Added 25 answers

We can find slope and y-intercept of a line by converting its equation to point slope form. In a point-slope form of equation y=mx+c, m (the coefficient of x variable) is the slope and c is the y-intercept of the line.
Now, 3x−y+18=0 can be written as y=3x+18 and hence its intercept on y-axis is 18.
Further 3x−2y+5=0 can be written as 2y=3x+5 or
y = 3 2 x + 5 2 and hence its slope is 3 2 .
Now as product of slopes of two perpendicular lines is −1, slope of line perpendicular to 3x−2y+5=0 (whose slope is 3 2 ) will be - 1 3 2 = - 1 × 2 3 = - 2 3 .
We now need to find the equation of a line whose slope is - 2 3 and intercept on y-axis is 18 and using slope intercept form of equation y=mx+c, this should be
y = - 2 3 x + 18 or 3 y = - 2 x + 54 or 2 x + 3 y - 54 = 0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?