Write an equation of the line that passes through (0, – 5) and is perpendicular to
the line y= - 4/5x

y=5/4x-5

Step-by-step explanation:

Hi there!

The equation of the line is typically written as y=mx+b, where m is the slope and b is the y intercept

Perpendicular lines have slopes that are negative and reciprocal. If they are multiplied together, the result is -1

So let's find the slope of the perpendicular line with this formula:

-4/5m=-1

multiply both sides by -5/4 (we need to isolate m onto one side, and -4/5*-5/4=1)

m=5/4

So the slope of the new line is 5/4

Here's the equation so far:

y=5/4x+b

now we need to find b

Because the equation of the line passes through (0,-5), we can use it to solve for b

substitute 0 as x and -5 as y

-5=5/4(0)+b

-5=0+b

-5=b

Therefore the equation of the line is:

y=5/4x-5

Hope this helps!