Find the slope that is perpendicular to the line 4x+5y=−5

limfne2c

limfne2c

Answered question

2022-10-14

Find the slope that is perpendicular to the line 4x+5y=−5

Answer & Explanation

Layne Murillo

Layne Murillo

Beginner2022-10-15Added 14 answers

Let's start with the original equation:
4 x + 5 y = - 5
From here, we can manipulate the equation into the slope-intercept form. We first move the 4x over to the right side by subtracting 4x from both sides:
5 y = - 5 - 4 x
Next, we divide both sides by 5 to isolate the y variable:
y = - 5 - 4 x 5
We then simplify the right portion of the equation:
y = - 5 5 - 4 x 5
And further simplification follows:
y = - 1 - 4 x 5
We then rearrange the entire equation to clearly show the equation in slope-intercept form:
y = - 4 x 5 - 1
Now that we have the equation in slope-intercept form, we can clearly see that - 4 5 is the slope here.
From here, it is easy. The product of a slope and its perpendicular slope is always −1. (Proof: perpendicular lines have negative reciprocal slope)
If we set a to be the perpendicular slope of - 4 5 , then
- 4 5 a = - 1
Then, we can isolate a by dividing by - 4 5 on both sides and then simplifying the result:
a = - 1 - 4 5 = - 1 - 5 4 = 5 4
Thus, the slope of the line perpendicular to the line 4x+5y=−5 is 5 4

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?