Reduce x*sqrt3 + y +2 = 0 to the slope intercept form and hence find its slope, inclination and y intercept.

Expert Answers
hala718 eNotes educator| Certified Educator

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

giorgiana1976 | Student

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. 

neela | Student

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.