Question

Find the slope and the y-intercept of the equation x − 4(y + 1) − 5 = 0.

Answer 1

@mathwizz16 can you help me?

Answer 2

Solve for y.
Start by distributing the 4.
Can you do that?

Answer 3

no not really..

Answer 4

Here is an example of the distributive property:

\(-3(x + 2)\)

\(= (-3)(x) + (-3)(2) \)

\(=-3x - 6\)

In your problem you have -4(y + 1) as part of your equation.
Can you follow my example above and try to do the same with -4(y + 1)?

Answer 5

-4y-3

Answer 6

Almost.
-4 * y = -4y, that is correct
-4 * 1 = -4, not -3
So -4(y + 1) = -4y - 4
Now we put that together with the rest of the problem

Answer 7

x − 4(y + 1) − 5 = 0
x - 4y - 4 - 5 = 0

Now we can combine the -4 and the -5 together.

Answer 8

x - 4y - 9 = 0

Answer 9

We need to solve for y, so we need to move everything, other that the term that has y in it, to the right side. Since x is +x, we subtract x from both sides. Since the 9 is -9, we add 9 to both sides.

Answer 10

x - 4y - 9 = 0
-x + 9 - x + 9
------------------------(add)
-4y = -x + 9

Now we have -4y = -x + 9

Since y is being multiplied by -4, we divide both sides by -4.

\(y = \dfrac{-x}{-4} + \dfrac{9}{-4} \)

\(y = \dfrac{1}{4}x - \dfrac{9}{4} \)

Now that we have the equation solved for y, we have it in the
y = mx + b form,
where m is the slope, and b is the y-intercept.