Question

If a line through the origin has a slope of 2, what is the slope of the line through the origin that is perpendicular to

Answer 1

Answer:

$-\frac{1}{2}$

Step-by-step explanation:

We have the slope value of the first line, we will call this $m_{1}$

so  $m_{1}=2$

And we use the condition so that two lines are perpendicular: the product of the two slopes must be equal to -1.

That is, if the slope of the first line is $m_{1}$ and the slope of the second line is $m_{2}$:

$m_{1*}m_{2}=-1$

we know that $m_{1}=2$, so:

$2m_{2}=-1$

and clearing for $m_{2}$:

$m_{2}=-\frac{1}{2}$

the slope of the line perpendicular to the line with a slope of 2 is: $-\frac{1}{2}$