Question

Write the equation of a line that is perpendicular to the given line and that passes through the given poin

-x + 5y = 14; (-5, -2)

Answer 1

y = 5x + 23

Explanation:

First, let's make the equation in the form: y = mx + b

Let's take x to the other side to avoid dealing with negatives, so now we have:

5y = x + 14

Divide everything by 5 that way, y can be alone.

y = 1/5x + 14/5

1/5 and 14/5 are fractions.

Now that we have our equation, let's put it in a perpendicular form.

When you make an equation perpendicular, remember that the coefficient of x will flip over, and b will be a different number. Since the number with x will flip, it'll become:

y = 5x + b

I took out 14/5 because we need to see what b will be with our new equation.

Let's plug in the given points, (-5, -2) to find b.

-2 = 5(-5) + b

-2 = -25 + b

Take -25 and add it on -2 to get rid of it, and to make b alone.

-2 + 25 = b

b = 23

Your perpendicular equation is:

y = 5x + 23

Answer 2

-x+ 5y= 14
5y= 14+x
Y= (14+x)/5
Y= 14/5+1/5x

Perpendicular equations have opposite reciprocal slopes

The opposite reciprocal slope of 1/5x is -5x.


-2= -5(-5)+ b
-2= 25+ b
B= -2-25
B= -27

The equation is y= -5x-27.

Hope this helps!