Question

Consider the equation -3x+4y=-12 A line parallel to the above line would have a slope of ()/(frac{3}{4}) what would A line perpendicular to the above line have a slope of?

Answer 1

`m=-(4)/(3)`

1) Perpendicular lines have reciprocal and opposite slopes. But to properly check it, we need to rewrite the Standard form to the Slope-intercept

So let's rewrite it:

`\begin{gathered} -3x+4y=-12 \\ 4y=-12+3x \\ y=-(12)/(4)+(3)/(4)x \\ y=(3)/(4)x-3 \end{gathered}`

2) Now, we can clearly see the slope. So now, we can tell that a perpendicular line would be reciprocal and opposite to the slope so we can tell that a perpendicular line will be:

`m=-(4)/(3)`