Answer:
y = -4x-21
Explanation:
Hi there!
We want to write an equation of the line that passes through (-4, -5) and is parallel to y=-4x-1.
Parallel lines have the same slopes. So let's find the slope of y=-4x-1.
The line is written in the form y=mx+b, where m is the slope and b is the y intercept.
As -4 is in the place of where m should be, -4 is the slope of y=-4x-1.
It's also the slope of the line parallel to that line.
Right now, what we know about the line parallel to y=-4x-1 is that the slope of it is 4 and it passes through the point (-4, -5).
We can substitute those values into the formula for point-slope form, which is y-y_1=m(x-x_1)y−y
1
=m(x−x
1
) , where m is the slope and (x_1, y_1)(x
1
,y
1
) is a point.
We can label the values of everything to help us avoid confusion.
m=-4
\begin{gathered}x_1=-4\\y_1=-5\end{gathered}
x
1
=−4
y
1
=−5
Now substitute those values into the formula. Note: the formula contains SUBTRACTION, and we have NEGATIVE numbers. Hence,
y--5=-4(x--4)y−−5=−4(x−−4)
Now simplify.
y+5=-4(x+4)y+5=−4(x+4)
On the right side, do the distributive property.
y+5=-4x-16
Subtract 5 from both sides.
y=-4x-21