Consider the line y=2x-8.

2 answers:

andrey2020 [161]4 years ago

8 0

Answer: The slope of a line parallel to this line is 2. The slope of a line perpendicular to this line is - $\frac{1}{2}$ .

Step-by-step explanation:

You know that your slope for this equation is 2, since that is your “m” in the slope-intercept equation, y = mx + b.

Lets split this into two parts.

Part 1: Finding the parallel slope

We know that the slopes of paralell lines are the same.Therefore, the slope of a line parallel to the one we know would also be 2!

Part 2: Finding the perpendicular slope

We also know that the slopes of perpendicular lines are opposite reciprocals, meaning the the sign (negative or positive) is changed, and the number is flipped over itself. As taught in my pre-algebra class, change the sign, flip the line.

Here is an example:

The opposite reciprocal of the number 5 is - $\frac{1}{5}$ . First, I changed the number to negative, then I figured out that 5 is technically $\frac{5}{1}$ , so I flipped that around.

Now, let’s get on to the real problem. If you do the math, the opposite reciprocal of 2 will be - $\frac{1}{2}$ . Therefore, that is your slope of that perpendicular lime.

Hope this helps! :)