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!

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

more detail

step-by-step explanation: