Reduce x*sqrt3 + y +2 = 0 to the slope intercept form and hence find its slope, inclination and y intercept.
x*sqrt3 + y + 2 = 0
The equation for the slope intercept form is:
y= mx + c where m is the slope
First we need y on the left side by itself, so we move all other terms.
==> y= -(sqrt3)*x - 2
Now we have a slope form equation for the line y where the slope m = - sqrt3 and the constant term c = -2
We'll have to reduce the given equation to the standard form:
y = mx + n, where m is the slope and n is the y intercept.
We'll write again the equation:
x*sqrt3 + y +2 = 0
We'll isolate y to the left side and we'll shift the constant and the term in x to the right side:
y = -(sqrt3)*x - 2
If we compare the resulted equation with the standard form of the equation, we'll get:
slope = m = -sqrt3
y intercept = n =-2
We know that the slope is the inclination of the line, which we'll note as a.
tan a = m = -sqrt3= -tan 60 = tan (180 - 60) = tan 120, so, the inclination a = 120 degrees.
y = mx+c is the form of a line.
The given equation of the line is x*sqrt3+y+2 = 0 . Subtract -(x*sqrt3 +2) from both sides:
y = -x*sqrt3 -2
This could be compared to y = mx+c. So comparing the coefficients of y, x and constant terms,
1/1 = (-sqrt3)/m = -2/c.
Therefore m = -sqrt3 and c = -2.
Therefore y = (-sqrt3)x+(-2) is the slope intercept form of the given equation.