Question

(b) Write the equation of the line which passes through the point(0, 2) and has a slope of
1/3​

Answer 1

Given :

• point : (0, 2)
• slope = 1/3

To find :

• equation of the line

Concept used :

$\sf \: Equation \: of \: line\: passing \: through \: a \: point \: (x_1 , y_1) \: and \: slope \: is \: \bf m : -$

$\implies \bf(y - y_1) = (x - x_1)m$

Solution :

$\sf \: Here :- \: \bf (x_1 , y_1) = \sf (0, 2) \: \\ \bf \: m \: = \sf \dfrac{1}{3}$

Now , we will find equation of line.

$\implies \bf(y - y_1) = (x - x_1)m$

$\sf \: Put :- \\ \sf \: \: \: x_1 = 0 \\ \sf y_1 = 2 \\ \sf m = \dfrac{1}{3}$

$\implies \sf(y - 2) = (x -0) \dfrac{1}{3}$

$\implies \sf(y - 2) = (x ) \dfrac{1}{3}$

$\implies \sf(y - 2) = \dfrac{x}{3}$

Now cross multiply :-

$\implies \sf3(y - 2) = x$

$\implies \sf3y - 6 = {x}$

$\implies \sf3y - 6 - x = 0$

Answer :

3y -x -6 = 0 is the equation of line which passes through the point(0, 2) and has a slope of

1/3.

Answer 2

The equation of the line is x-3y+6=0.

Given:

• A line passes through the point (0,2)
• It has a slope 1/3.

To find:

• Find the equation of line.

Solution:

Formula/concept to be used:

• If a line passes through a point $P(x_1,y_1)$ and it has slope m, then the equation of line is $\bf y-y_1= m(x-x_1)$

Step 1:

Write the given values.

The point is (0,2), from which the line passes.

The slope of line, $m = \frac{1}{3}$

Step 2:

Find the equation of line.

Put the values in the equation of point-slope form.

$y - 2 = \frac{1}{3} (x - 0)$

$y - 2 = \frac{x}{3}$

$3y - 6 = x$

$- x + 3y = 6$

$\bf x - 3y = - 6$

Thus,

The equation of the line is x-3y+6=0.

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