Question

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

Answer 1

$\bigstar \underline{\underline{\sf Given:-}}$

• A straight line is  passing  through the point (1, 2) and parallel to the  line y = 3x + 1 .

$\bigstar \underline{\underline{\sf To\ find:-}}$

• Equation of the straight line.

$\bigstar \underline{\underline{\sf Solution:-}}$

Knowledge required:

❥General equation of a line is y=mx+c.

Where,

=> m = gradient,

❥ If two lines are perpendicular , m1.m2=-1

-----------------------

Acc to question,

Given line is y=3x+1.

∴ m = 3

Given that two lines are perpendicular,

$\implies \sf m_1 .m_2 = -1\\\\\implies \sf 3(m_2)=-1\\\\\implies m_2 =-1/3$

Therefore,slope of line perpendicular to y=3x+1 is -1/3.

The equation of line  :

$\implies \sf y=-\frac{1}{3} x+c$

$:\implies \sf 3y+x=c$

Given,the line passes through (1,2).

$:\implies \sf 3(2)+1=c\\\\:\implies 6+1=c\\\\:\implies\bold{ c=7}$

Therefore,

$\implies \sf x+3y=7\\\\\implies \boxed{\boxed{\sf x+3y-7=0.}}$

Hence,the equation of straight line passing  through the point (1, 2) and parallel to the  line y = 3x + 1 is​ x+3y-7=0.

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HOPE IT HELPS !

Answer 2

$\bigstar \underline{\underline{\sf Given:-}}$

A straight line is  passing  through the point (1, 2) and parallel to the  line y = 3x + 1 .

$\bigstar \underline{\underline{\sf To\ find:-}}$

Equation of the straight line.

$\bigstar \underline{\underline{\sf Solution:-}}$

Knowledge required:

❥General equation of a line is y=mx+c.

Where,

=> m = gradient,

❥ If two lines are perpendicular , m1.m2=-1

-----------------------

Acc to question,

Given line is y=3x+1.

∴ m = 3

Given that two lines are perpendicular,

$\implies \sf m_1 .m_2 = -1\\\\\implies \sf 3(m_2)=-1\\\\\implies m_2 =-1/3$

Therefore,slope of line perpendicular to y=3x+1 is -1/3.

The equation of line  :

$\implies \sf y=-\frac{1}{3} x+c$

$:\implies \sf 3y+x=c$

Given,the line passes through (1,2).

$:\implies \sf 3(2)+1=c\\\\:\implies 6+1=c\\\\:\implies\bold{ c=7}$

Therefore,

$\implies \sf x+3y=7\\\\\implies \boxed{\boxed{\sf x+3y-7=0.}}$

Hence,the equation of straight line passing  through the point (1, 2) and parallel to the  line y = 3x + 1 is x+3y-7=0.

-------------------------------

HOPE IT HELPS !