Which of the following two lines are parallel (pick 2)(1 point) Responses 3x + y = -2 3x + y = -2 2y - 6x = 4 2y - 6x = 4 2y = -6x - 8 2y = -6x - 8
The parallel lines are:
1) 3x + y = -2
2) 3x + y = -2
pick one of the other two
The parallel lines are:
1) 3x + y = -2
2) 2y - 6x = 4
To determine which two lines are parallel, we need to compare the slopes of the lines. Two lines are parallel if and only if their slopes are equal.
Let's convert the equations to slope-intercept form (y = mx + b), where m represents the slope.
1. Equation 1: 3x + y = -2
Rearranging to slope-intercept form: y = -3x - 2
Slope of Equation 1: -3
2. Equation 2: 2y - 6x = 4
Rearranging to slope-intercept form: y = 3x + 2
Slope of Equation 2: 3
3. Equation 3: 2y = -6x - 8
Rearranging to slope-intercept form: y = -3x - 4
Slope of Equation 3: -3
Based on the slopes, we can see that Equation 1 and Equation 3 have the same slope of -3. Therefore, the two parallel lines are:
1. 3x + y = -2
2. 2y = -6x - 8
To determine which of the given lines are parallel, we need to compare their slopes. The slope-intercept form of a linear equation is given as y = mx + c, where m represents the slope. Two lines are parallel if and only if they have the same slope.
Let's compare the slopes of the given lines:
1. The first equation is 3x + y = -2.
To find the slope, we need to rewrite the equation in slope-intercept form:
y = -3x - 2.
Comparing this equation with y = mx + c, we can see that the slope is m = -3.
2. The second equation is 2y - 6x = 4.
Rearranging the equation in slope-intercept form:
2y = 6x + 4,
y = 3x + 2.
Comparing this equation with y = mx + c, we can see that the slope is m = 3.
3. The third equation is 2y = -6x - 8.
Dividing through by 2 to get the equation in slope-intercept form:
y = -3x - 4.
Comparing this equation with y = mx + c, we can see that the slope is m = -3.
From the above analysis, we can conclude that the first line (3x + y = -2) and the third line (2y = -6x - 8) are parallel.