Question

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

Answer 1

See a solution process below:

Explanation:

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]}

Answer 2

graph{-4y-3x=4 [-10, 10, -5, 5]}

Explanation:

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.