Question

Write an equation for the line that passes through (-4,-5) and is perpendicular to y=1/4x-10

Answer 1

What is the slope of the given equation?

Answer 2

That's all it says

Answer 3

When an equation is written in the form:
y = mx + b
m is the slope.

Answer 4

In your case, the equation is y = (1/4)x - 10
You have 1/4 multiplying x just like in the form above we have m multiplying x.
The slope is m, so the slope of the line is 1/4

Answer 5

Yeah I got that far. I don't know what equation to write

Answer 6

Ok. The line we are give has a slope of 1/4
The slopes of perpendicular lines are negative reciprocals.
That means that the slopes of perpendicular lines multiply to -1.

Answer 7

That also means that if you know the slope of a line and you need the slope of a perpendicular, just take the given slope, write it as a fraction, flip the fraction, and change the sign.

Answer 8

The given line has slope 1/4. That is already a fraction.
Now flip the fraction: 4/1 which is the same as 4.
Now change the sign: 4 becomes -4.

Answer 9

That means the libe we need has a slope of -4

Answer 10

Now we know the perpendicular will be:
y = -4x + b
We need to find b.

Answer 11

We now use the point (-4, -5).
We replace x and y by -4 and -5, respectively, and solve for b.
-5 = -4(-4) + b

Answer 12

-5 = 16 + b
-21 = b
y = -4x - 21 is the equation we were looking for.

Answer 13

See now i remember this, thank you so much.

Answer 14

You're welcome.