Yay, calc
we need to take take the implicit derivitive
to evaluate the slope, we need the point
when the line crosses the x axis, the value of y is 0
find the x value when y=0 to find the point, (x,0)
0+0+4x=8
4x=8
x=2
(2,0) Is the point
so
the derivitive is
minus 2xy both sides
minus 4 both sides
undistribute dy/dx
divide both sides by x²+3y²
now find the slope at the point (2,0)
sub 2 for x and 0 for y
slope is -1
use point slope form
the equation of a line that has a slope of m and passes through the point (x1,y1) is y-y1=m(x-x1)
slope is -1 and point is (2,0)
y-0=-1(x-2)
y=-1(x-2)
or
y=-x+2