find the equation of a line passing through the point (2,1) and which is perpendicular to the line

3x+2y-5=0

find the equation of a line passing through the point (2,1) and which is perpendicular to the line

3x+2y-5=0

Tutors, please sign in to answer this question.

Saugus, MA

3x+2y-5=0

2y=-3x+5

y=(-3/2)x+(5/2)

slope of this line is -3/2

a line perpendicular to this line will have a slope that is the negative reciprocal of (-3/2)

the slope of the perpendicular line is 2/3

y-1=(2/3)(x-2)

y-1=(2/3)x-(4/3)

y=(2/3)x+1-(4/3)

y=(2/3)x-(1/3)

or you can use y=mx+b

y=(2/3)x+b

1=(2/3)(2)+b

1=(4/3)+b

1-(4/3)=b

-1/3=b

y=(2/3)x-(1/3)

Middletown, CT

Hi Dalia;

3x+2y-5=0

We need the equation in the format of y=mx+b for which m=slope, and b is the y-intercept, the value of y when x=0.

3x+2y-5=0

Let's add 5 to both sides...

5+3x+2y-5=0+5

3x+2y=5

Let's subtract 3x from both sides...

-3x+3x+2y=-3x+5

2y=-3x+5

Let's divide both sides by 2...

(2y)/2=[(-3x)/2]+(5/2)

y=(-3/2)x+(5/2)

The slope of this line is -3/2.

The slope of the line perpendicular to such is positive 2/3.

y=2/3x+b

The y-intercept, b, is unknown at this time.

Let's plug-in the one coordinate provided to establish such; (2,1).

1=[(2/3)(2)]+b

1=(4/3)+b

Let's subtract 4/3 from both sides...

-4/3+1=(4/3)+b-(4/3)

-1/3=b

y=(2/3)x-(1/3)

Anthony G.

Love math and science and passionate about teaching what I know

Orange, NJ

4.7
(345 ratings)

Sagar P.

Mathlete to help with Middle and High School Math and SAT Math

New York, NY

4.0
(1 ratings)

Christopher W.

High School Math Teacher tutoring math and SAT prep

Cranford, NJ

5.0
(20 ratings)

## Comments