Question

What is the slope of a line perpendicular to the line y=2x+5 ?What is the slope of a line perpendicular to the line y=2x+5 ?

Answer 1

Answer:

$-\frac{1}{2}$

Step-by-step explanation:

Hi there!

In the given equation $y=2x+5$, the slope of the line is 2.

Perpendicular lines always have slopes that are negative reciprocals, like negative "flipped" fractions.

Example: The negative reciprocal of $\frac{3}{1}$ (which is the same as 3) is $-\frac{1}{3}$.

Example 2: The negative reciprocal of $-\frac{4}{3}$ is $\frac{3}{4}$.

Using this logic, the negative reciprocal of 2, or $\frac{2}{1}$, is $-\frac{1}{2}$. Therefore, the slope of a line perpendicular to the line $y=2x+5$ is $-\frac{1}{2}$.

I hope this helps!