Answer:
[tex]\displaystyle \perp\:\frac{1}{2} \\ \parallel\:-2[/tex]
Step-by-step explanation:
You must first transform this standard equation to a Slope-Intercept equation like so:
[tex]\displaystyle y = mx + b \\ \\ -6x - 3y = -5 \hookrightarrow \frac{-3y}{-3} = \frac{6x - 5}{-3} \\ \\ \boxed{y = -2x + 1\frac{2}{3}}[/tex]
So, from this equation, we can tell that the y-intercept is at [tex]\displaystyle [0, 1\frac{2}{3}],[/tex]and the rate of change [slope] is −2, which is represented by [tex]\displaystyle m.[/tex]Now, we want the information on the rate of change ONLY. Perpendicular graphs have OPPOCITE MULTIPLICATIVE INVERCE rate of changes, which means we take the oppocite of −2, then flip it, to get [tex]\displaystyle \frac{1}{2}.[/tex]Parallel equations have SIMILAR rate of changes, so −2 remains as is.
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