Question

How do you graph `x-2y=3`?

Answer 1

graph{x-2y=3 [-10, 10, -5, 5]}

Explanation:

Method 1:
Given `x-2y=3`, we can write the equation in slope-intercept form `y=mx+b` where m = the slope, and b = the y-intercept.

To do this, we need to isolate the y.
Subtract x from both sides:
`-2y = 3-x`
Divide everything by -2:
`y=-3/2+1/2x`
Rearrange right-hand side to get `y=mx+b`"
`y=1/2 x-3/2`

In this situation, the slope `m=1/2` and the y-intercept `b=-3/2`
The y-intercept means that the graph will intersect the y-axis (the vertical axis) at the point `(0,-3/2)`.
The slope is equivalent to `"rise"/"run"`, therefore the graph will "rise" 1 point upwards and "run" 2 points to the right from the y-intercept.
Since we know the slope and y-intercept, we also know that `(0+2,-3/2+1) = (2,-1/2)` will also be on the line.

Method 2:
Alternatively, you can find the graph of this line by finding the x-intercept `(x,0)` and y-intercept `(0,y)`.

To find the x-intercept, set `y = 0`:
`x-2(0)=3 hArr x=3`
The x-intercept is `(3,0)`.

To find the y-intercept, set `x=0`:
`0-2(y)=3 hArr -2y=3 hArr y=-3/2`
The y-intercept is `(0,-3/2)`

Plot the x-intercept and y-intercept and connect both points.