Because this equation is in slope-intercept form we can find the #x#-intercept and #y#-intercept directly from the equation. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope, #color(blue)(b)# is the y-intercept value and #color(blue)(-b)/color(red)(m)# is the x-intercept..

#y = color(red)(-6)x - color(blue)(9)#

Therefore the #y#-intercept is: #color(blue)(b = -9)# or #(0, color(blue)(-9))#

And, the #x#-intercept is:

#color(blue)(- -9)/color(red)(-6) => color(blue)(9)/color(red)(-6) => -color(blue)(3 xx 3)/color(red)(3 xx 2) => -color(blue)(color(black)(cancel(color(blue)(3))) xx 3)/color(red)(color(black)(cancel(color(red)(3))) xx 2) => -3/2#

Or

#(-3/2, 0)

We can next plot the two points on the coordinate plane:

graph{(x^2+(y+9)^2-0.3)((x+ 3/2)^2+y^2-0.3)=0 [-30, 30, -15, 15]}

Now, we can draw a straight line through the two points to graph the line:

graph{(y+6x+9)(x^2+(y+9)^2-0.3)((x+ 3/2)^2+y^2-0.3)=0 [-30, 30, -15, 15]}