Question

Find the equation of the line passing through the point (-2,3) and inclined with x-axis at angle 60°.

Answer 1

tan 60=slope
slope =root3
m=root3
point(-2,3)
y-3= root3(x+2)
root3x + 2root3 -y+3=0
root3x -y+ 2root3+3=0

Answer 2

The equation of the line is $y-3=\sqrt3(x+2)$

Step-by-step explanation:

Given:

The point on the line is $(-2,3)$.

The line makes an angle of 60°.

The slope of a line is given as the tangent of the angle the line makes with the x axis.

Here, the line makes an angle of 60°. Therefore, the slope is given as:

$m=\tan \theta\\m=\tan (60\°)\\m=\sqrt3$

Now, a line with a given point $(x_1,y_1)$ and slope $m$ is given as:

$y-y_1=m(x-x_1)$

Plug in $x_1=-2,y_1=3,m=\sqrt3$. This gives,

$y-3=\sqrt3(x-(-2))\\\\y-3=\sqrt3(x+2)$

Therefore, the equation of the line in the point-slope form is:

$y-3=\sqrt3(x+2)$