Which of the following is parallel to the line: 4x+2y=-3?
a) 4x+3=2y+3 c) 1/4x+1/2y=1/3
b) 6x+3y=-3 d) 2x-4y=6
To determine which of the given options is parallel to the line 4x + 2y = -3, we need to compare the slopes of the lines. The slope-intercept form of a linear equation is y = mx + b, where "m" represents the slope of the line.
First, let's rearrange the equation 4x + 2y = -3 into slope-intercept form:
4x + 2y = -3
2y = -4x - 3
y = -2x - (3/2)
The slope of the line is -2. Any line with the same slope of -2 will be parallel to the given line.
Let's look at the options:
a) 4x + 3 = 2y + 3
Rearranging the equation, we get:
2y = 4x
y = 2x
The slope of this line is 2, which is not the same slope as the given line. Therefore, it is not parallel.
b) 6x + 3y = -3
Rearranging the equation, we get:
3y = -6x - 3
y = -2x - 1
The slope of this line is -2, which is the same slope as the given line. Therefore, it is parallel.
c) (1/4)x + (1/2)y = 1/3
Rearranging the equation, we get:
(1/2)y = (-1/4)x + (1/3)
y = (-2/4)x + (2/3)
y = (-1/2)x + (2/3)
The slope of this line is -1/2, which is not the same slope as the given line. Therefore, it is not parallel.
d) 2x - 4y = 6
Rearranging the equation, we get:
-4y = -2x + 6
y = (1/2)x - (3/2)
The slope of this line is 1/2, which is not the same slope as the given line. Therefore, it is not parallel.
Therefore, the only line among the options that is parallel to the line 4x + 2y = -3 is option b) 6x + 3y = -3.