How do you graph #-4y-3x=4#?

First, solve for two points which solve the equation and plot these points:

First Point: For #x = 0#

#-4y - (3 xx 0) = 4#

#-4y - 0 = 4#

#-4y = 4#

#(-4y)/color(red)(-4) = 4/color(red)(-4)#

#y = -1# or #(0, -1)#

Second Point: For #x = 4#

#-4y - (3 xx 4) = 4#

#-4y - 12 = 4#

#-4y - 12 + color(red)(12) = 4 + color(red)(12)#

#-4y - 0 = 16#

#-4y = 16#

#(-4y)/color(red)(-4) = 16/color(red)(-4)#

#y = -4# or #(4, -4)#

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

graph{(x^2+(y+1)^2-0.035)((x-4)^2+(y+4)^2-0.035)=0 [-10, 10, -5, 5]}

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

graph{(-4y-3x-4)(x^2+(y+1)^2-0.035)((x-4)^2+(y+4)^2-0.035)=0 [-10, 10, -5, 5]}

Convert the equation #-4y-3x=4# into slope-intercept form to make it easier to graph.
Remember, slope-intercept form is #y=mx+b#, where #m# stands for slope and #b# stands for y-intercept.
This means you need to isolate #y# in this equation #-4y-3x=4#.
Add #3x# to both sides, which will give you #-4y=3x+4#.
Divide by #-4# on both sides and you will get #y=-3/4x-1#.
This means the y-intercept is -1 and the slope is #-3/4#.
On the graph, place a dot on #(0, -1)# since that is the y-intercept and where you will start the graph.
Remember, slope is #(rise)/(run)#. So in this case, you go up 3 and to the left 4 starting from the y-intercept. And you go down 3 and to the right 4 starting from the y-intercept.