Question

Find an equation of the line that is parallel to the graph of 2x+3y=5 and contains the point (3, −1).


Find an equation of the line passing through each of the following pairs of points.
5,6 3,4
cFind an equation of the line passing through each of the following pairs of points.
d
(0, 7), (0, −8)




Find an equation of the line passing through each of the following pairs of points.

e

(−8, −3), (−1, −2)

Answer 1

Answer:

A) Equation of line is 3X - 2Y = 11

B) Equation of line is Y = X + 1  

C) Equation of line is Y - 7 = 0

Equation of line , point (3 , -1) and slop $\frac{3}{2}$ is 3X - 2Y = 11

Step-by-step explanation:

Given equation of line as  2x + 3y = 5

slove of this line (m1) = - $\frac{2}{3}$

Now another line passes through point  (3 , -1) having slop (m2)

Both lines are parallel to each other, i.e (m1) × (m2) = - 1

So slop of second line (m2 ) = $\frac{-1}{m1}$

                                      (m2) = $\frac{-1}{(\frac{-2}{3} } )$

                                      (m2) = $\frac{3}{2}$

Now eq of line with point (3 , -1) and slop (m2)

Y- y1 = (m2)( X - x1)

Or, Y +1 = $\frac{3}{2}$ (X - 3)

i.e 2Y + 2= 3X - 9

∴ Equation of line is 3X - 2Y = 11     Answer

B) Given points as ( 5,6) and (3 , 4)

Slop (m) = $\frac{y2 - y1}{x2 - x1}$ = $\frac{4 - 6}{3 - 5}$ = 1

So the equation of line is

Y- y1 = (m)( X - x1)

Y - 6 = (1) (X - 5)

i.e Equation of line is Y = X + 1   Answer

C) Given points as ( 0, 7)  , (0 , -8)

Slop (m) with co-ordianate =  $\frac{y2 - y1}{x2 - x1}$

Or,                                        =  $\frac{-8 - 7}{0 - 0}$

                                            =0

Hence equation of line is Y - 7 = 0     Answer