Question

The equation of a straight line passing through the point (1,2)and inclined at 45degrees to the line y=2x+1

Answer 1

tan45=(m-1/2)/(1+m/2)
1+m/2=m-1/2. tan45=1
3/2=m/2
m=3

slope of required lime=3
using 1 point form,

3=(y-2)/(x-1)
3x-3=y-2
3x-y-1=0

is our required equation

Answer 2

Concept: A straight line's general equation is $y = mx + c$, where m is the gradient and $y = c$  is the value at which the line intersects the $y$-axis. On the $y$-axis, this quantity $c$ is known as the intercept.

Given:

Equation of straight-line pass-through $(1,2)$

$\theta= 45°$, inclination to $y=2x+1$

To find:

equation of a straight line

Solution:

Let the equation of the straight line be $y = mx + c$

The angle between two lines is given by

$tan \theta =\frac{m_{2} - m_{1} }{1 + m_{1} m_{2} }$

$tan45^{\°}=\frac{m-2}{1+2m}\\ m-2=2m+1\\m=-3$

Therefore, the value of $y=-3x+c$.

Value of $c=2+3=5$

The equation of a straight line is $y+3x=5$.

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