Question

The equation of the line passing through (1,2) and parallel to 3x+2y+7=0 is

Answer 1

Question:

Find the equation of the line passing through the point (1,2) and parallel to

3x + 2y + 7 = 0.

Note:

1) Point-slope form of a straight line:

The equation of straight line passing through a given point (x1,y1) and having the slope "m" is given by;

(y-y1)/(x-x1) = m

OR

(y-y1) = m(x-x1)

2) Slope-y-intercept form of a straight line :

The equation of a straight line with the slope "m" and y-intercept "c" is given by;

y = mx + c

Solution:

Here ,

The equation of the given line is:

3x + 2y + 7 = 0.

ie;

=> 2y = - 3x - 7

=> y = - 3x/2 - 7/2

=> y = (-3/2)x + (-7/2)

{ This is the slope-y-intercept form of the given line. }

Now,

Comparing the above equation with the Slope-y-intercept form of the straight line (ie ; y = mx + c) , we get ;

slope ,(m) = -3/2

y-intercept ,(c) = -7/2

Also,

It is given that , the required line is parallel to the given line ,3x+2y+7 = 0

Thus,

Slope of the required line is equal to the slope of the given line.

ie; For the required line, m = -3/2

Also,

It is given that , the required line passes through the point (1,2).

Thus, we can consider that;

x1 = 1

y1 = 2.

Now,

As per the Point-slope form of a straight line ; the equation of required line with slope " m = -3/2 " and passing through the given point (x1=1,y1=2) , will be given by;

=> (y-y1) = m(x-x1)

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

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

=> 2y - 4 = -3x + 3

=> 2y - 4 + 3x - 3 = 0

=> 3x + 2y - 7 = 0

Hence,

The equation of the required line is :

3x + 2y - 7 = 0.

Answer 2

Answer: 3x + 2y = 7

Step-by-step explanation:

Let the slop of the required line be m₁ and it passed through the point (x₁ ,y₁)

Given that equation of the line passes through a point (1,2)

(x₁ , y₁) = (1, 2)

Now, we shall find the slop of the line 3x + 2y + 7 = 0,

Let the slop of this line be m₂.

m₂ = -(Coefficient of x)/(Coefficient of y)

m₂ = -(3/2)

Now, its given that required line is parallel to this given line. Therefore, slop of both lines will be equal, i.e.

m₁ = m₂

m₁ = -3/2

We know that equation of the line passing through (x₁ , y₁) having slop m₁ is given by,

y - y₁ = m(x - x₁)

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

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

2y - 4 = -3x + 3

2y + 3x = 3 + 4

3x + 2y = 7

This is the required equation of  the line.