Question

Which of the following lines passes through the origin and is inclined to the X-axis by 45
∘
?

Answer 1

Step-by-step explanation:

Given

slope(m)= tanθ

θ→ inclination with +ive x axis

Here θ=45

o

m=tan(45

o

)=1

Also, the slope intercept form of Eq

n

is y=mx+c

But c intercept on y axis

So here, it passes through the point (3,0) with slope 1

∴y=1(x−3)

Or, x−y−3=0

Answer 2

The equation of the line is x - y = 0

Given :

A line passes through the origin and is inclined to the X-axis by 45°

To find :

The equation of the line

Solution :

Step 1 of 2 :

Find slope of the line

Here the given line is inclined to the X-axis by 45°

So we have θ = 45°

Slope of the line

= m

= tan θ

= tan 45°

= 1

Step 2 of 2 :

Find the equation of the line

Now the line passes through the origin

Hence the required equation of the line is

$\displaystyle \sf{ (y - 0) = 1(x - 0)}$

$\displaystyle \sf{ \implies y = x}$

$\displaystyle \sf{ \implies x - y = 0}$

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