Question

How do you graph `6x-4y=16`?

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`

`(6 * 0) - 4y = 16`

`0 - 4y = 16`

`-4y = 16`

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

`y = -4` or `(0, -4)`

Second Point:

For `x = 2`

`(6 * 2) - 4y = 16`

`12 - 4y = 16`

`-color(red)(12) + 12 - 4y = -color(red)(12) + 16`

`0 - 4y = 4`

`-4y = 4`

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

`y = -1` or `(2, -1)`

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

graph{(x^2+(y+4)^2-0.08)((x-2)^2+(y+1)^2-0.08)=0 [-20, 20, -10, 10]}

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

graph{(6x-4y-16)(x^2+(y+4)^2-0.08)((x-2)^2+(y+1)^2-0.08)=0 [-20, 20, -10, 10]}