Question

How do you graph `4x - 3y = 6`?

Answer 1

Find the intercepts with the two axes and draw a line through it.

Explanation:

Given:

`4x-3y=6`

Since this equation contains just linear or constant terms, it describes a straight line.

If we put `x=0` or equivalently cover up the term `4x`, then we get:

`-3y=6`

Dividing both sides by `-3`, this becomes:

`y = -2`

So the line passes through `(0, -2)`

If we put `y=0` or equivalently cover up the term `-3y`, then we get:

`4x=6`

Dividing both sides by `4`, this becomes:

`x = 6/4=3/2`

So the line passes through `(3/2, 0)`

Now we can draw our line through these two intercepts:

graph{(4x-3y-6)(x^2+(y+2)^2-0.005)((x-3/2)^2+y^2-0.005)=0 [-5.17, 4.83, -3.42, 1.58]}

Answer 2

Refer to the explanation for the process.

Explanation:

Graph:

`4x-3y=6` is the standard form for a linear equation.

We can graph it by solving for the x-intercept `(x,0)` and y-intercept `(0,y)`. We only need two points to plot a straight line from a linear equation.

X-Intercept

Set `y=0` and solve for `x`.

`4x-3(0)=6`

`4x=6`

Divide both sides by `4`.

`x=6/4`

Simplify.

`x=3/2`

x-intercept: `(3/2,0)`

Y-Intercept

Set `x=0` and solve for `y`.

`4(0)-3y=6`

`-3y=6`

Divide both sides by `-3`.

`y=-6/3`

Simplify.

`y=-2`

y-intercept: `(0,-2)`

Plot the x- and y-intercepts on a grid and draw a straight line between the points.

graph{4x-3y=6 [-10, 10, -5, 5]}