- Slope-Intercept Form: y = mx + b, with m = slope and b = y-intercept
So remember that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals to each other. But first, we have to find out the slope of the original equation. The easiest method to find the slope is to convert this standard form equation to slope-intercept form.
Firstly, subtract 6x on both sides of the equation: [tex]-4y=-6x-3[/tex]
Next, divide both sides by -4 and your slope-intercept form is [tex]y=\frac{3}{2}x+\frac{3}{4}[/tex]
Now, looking at our slope-intercept form we see that the slope of the original equation is 3/2. Using what we know about parallel and perpendicular lines, the slope of a parallel line is 3/2 and the slope of a perpendicular line is -2/3
