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

1 Answer
May 14, 2018

Answer:

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.