Question

How do you graph `4x=2y+6` using the x and y intercepts?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the `x` and `y` intercepts.

x-intercept

Set `y` equal to `0` and solve for `x`:

`4x = (2 * 0) + 6`

`4x = 0 + 6`

`4x = 6`

`(4x)/color(red)(4) = 6/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 3/2`

`x = 3/2`

`(3/2, 0)`

x-intercept

Set `x` equal to `0` and solve for `y`:

`4 * 0 = 2y + 6`

`0 = 2y + 6`

`0 - color(red)(6) = 2y + 6 - color(red)(6)`

`-6 = 2y + 0`

`-6 = 2y`

`-6/color(red)(2) = (2y)/color(red)(2)`

`-3 = (color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2))`

`-3 = y`

`(0, -3)`

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

graph{(x^2+(y+3)^2-0.025)((x-(3/2))^2+y^2-0.025)=0 [-10, 10, -5, 5]}

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

graph{(4x-2y-6)(x^2+(y+3)^2-0.025)((x-(3/2))^2+y^2-0.025)=0 [-10, 10, -5, 5]}