How do you graph x-2y=3?

May 14, 2018

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

Explanation:

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

To do this, we need to isolate the y.
Subtract x from both sides:
$- 2 y = 3 - x$
Divide everything by -2:
$y = - \frac{3}{2} + \frac{1}{2} x$
Rearrange right-hand side to get $y = m x + b$"
$y = \frac{1}{2} x - \frac{3}{2}$

In this situation, the slope $m = \frac{1}{2}$ and the y-intercept $b = - \frac{3}{2}$
The y-intercept means that the graph will intersect the y-axis (the vertical axis) at the point $\left(0 , - \frac{3}{2}\right)$.
The slope is equivalent to $\text{rise"/"run}$, 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 $\left(0 + 2 , - \frac{3}{2} + 1\right) = \left(2 , - \frac{1}{2}\right)$ will also be on the line.

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

To find the x-intercept, set $y = 0$:
$x - 2 \left(0\right) = 3 \Leftrightarrow x = 3$
The x-intercept is $\left(3 , 0\right)$.

To find the y-intercept, set $x = 0$:
$0 - 2 \left(y\right) = 3 \Leftrightarrow - 2 y = 3 \Leftrightarrow y = - \frac{3}{2}$
The y-intercept is $\left(0 , - \frac{3}{2}\right)$

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