Which pair of lines are parallel? Select all that apply.
A.y=3-2x
y=2x-3
B.y=2x-1
y-2x=8
C. y-4x=6
y+4x=-6
D. y=-3x+1
y+4x=x-1
I think that its A and D
write in form y = m x + b
if m is the same, same slope, parallel
eg
A.y=3-2x
y=2x-3
====================
that is
y = -2 x + 3
y = +2 x - 3
-2 is NOT +2 !!!
NOT parallel
B. works m = 2
To determine if two lines are parallel, we need to compare their slopes. If the slopes of two lines are equal, then they are parallel.
Let's start by finding the slopes of the given lines:
A. For the first pair of lines:
Line 1: y = 3 - 2x
The slope of this line can be determined by comparing the coefficients of x, which is -2 in this case.
Line 2: y = 2x - 3
The slope of this line can be determined by comparing the coefficients of x, which is 2 in this case.
Hence, the slopes of the two lines are -2 and 2, respectively.
B. For the second pair of lines:
Line 1: y = 2x - 1
The slope of this line can be determined by comparing the coefficient of x, which is 2 in this case.
Line 2: y - 2x = 8
We need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope. Adding 2x to both sides, we get y = 2x + 8.
The coefficient of x, which is 2, represents the slope of this line.
Therefore, the slopes of the two lines in this pair are both 2.
C. For the third pair of lines:
Line 1: y - 4x = 6
We need to rearrange this equation in slope-intercept form. Adding 4x to both sides, we get y = 4x + 6.
The coefficient of x, which is 4, represents the slope of this line.
Line 2: y + 4x = -6
Rearranging this equation, we get y = -4x - 6.
The coefficient of x, which is -4, represents the slope of this line.
So, the slopes of the two lines in this pair are 4 and -4, respectively.
D. For the fourth pair of lines:
Line 1: y = -3x + 1
The slope of this line is -3.
Line 2: y + 4x = x - 1
Rearranging this equation, we get y = -3x - 1.
The coefficient of x, which is -3, represents the slope of this line.
Now, let's compare the slopes:
A. The slopes are not equal, so the lines are not parallel.
B. The slopes are equal (both 2), so the lines are parallel.
C. The slopes are not equal, so the lines are not parallel.
D. The slopes are equal (both -3), so the lines are parallel.
Therefore, the correct pairs of lines that are parallel are B and D.