Inequality Equation?

Question

The equation:

Y+1= -4(x-2)
-12x-3Y+21=0

represent:
A. same line
b. Parallel Line
C. Perpendicular Line
D. None

Answer 1

y + 1 = -4(x - 2)

y + 1 = - 4x + 8

y = 1 - 1 = - 4x + 8 - 1

y = - 4x + 7

- - - - - - - - - - -

- 12x - 3y + 21 = 0

- 12x - 3y + 21 - 21 = 0 - 21

- 12x - 3y = - 21

- 12x - 3y + 12x = 12x - 21

- 3y= 12x - 21

- 3y / - 3 = 12x / - 3 - 21 / - 3

y = 12x / - 3 - 21 / - 3

y = - 4x + 7

- - - - - - - - - - -- -

The slope and y intercept are the same. They are on the same line

- - - - - - - - -s-

Answer 2

An inequality is not an equation.
Both sides of an equation have the same value.
Both sides of an inequality usually do not.

You mean a SYSTEM of equation.

First, get the equations in the form y = mx + b
y+1=(-4)(x-2)
First multiply out the right side
y+1 = -4x +8
Next add -1 to both sides
y = -4x +7

Ok, now look at the second equation
-12x-3y+21 = 0
We can multiply both sides by 1/3
-4x - y + 7 = 0
Add -7 to both sides
-4x -y = -7
Multiply both sides by -1
4x + y = 7
Add -4x to both sides
y = -4x + 7

Hint... if you get the equations for lines in the form y = mx + b
m is said to be the "slope" of the line
b is said to be the "y intercept", i.e., the point at which it crosses the y axis.

If the slopes of lines are the same, they are parallel. If lines are parallel and have the same y-intercept, they are the same line.

Since the formula for the first line is the same as that of the second, they represent the same line.

Answer 3

Y+1= -4(x-2)
y + 1 = -4x + 8
y = -4x + 7

-12x-3Y+21=0
-3y + 21 = 12x
-3y = 12x - 21
y = -4x + 7

same line

Answer 4

y+1 = -4(x-2)
-12x-3y+21=0

I would put both of these into y=mx+b format

y+1=-4(x-2)
y+1=-4x+8
y=-4x+7

-12x-3y+21=0
-12x+21=3y
-4x+7=y

You will not that they are now the same equation, so A is correct.

Answer 5

it's the same line. You need to put both equations in the same form and simplify.

If you move the variables around to the form Y=mx+b, you'll see both are Y=-4x+7.