Tell whether the lines for each pair of equation are parallel, perpendicular or neither y=-1/2x-12
-6x-12y=21
To determine if two lines are parallel or perpendicular, we can compare the slopes of the lines.
First, let's rearrange the second equation to slope-intercept form (y = mx + b):
-6x - 12y = 21
-12y = 6x + 21
y = -1/2x - 7/2
From the rearranged equation, we can see that the slope of the second line is -1/2.
The slope of the first line, y = -1/2x - 12, is also -1/2.
Since the slopes of both lines are the same, the lines are parallel.
To determine whether the lines described by these equations are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of an equation of a line is given by y = mx + b, where m represents the slope of the line.
For the first equation, y = -(1/2)x - 12, we can see that the slope, m1, is -1/2.
Now we need to rearrange the second equation, -6x - 12y = 21, to the slope-intercept form.
We can start by isolating y:
-12y = 6x + 21
Dividing both sides of the equation by -12:
y = -(1/2)x - (7/2)
Comparing this equation to the slope-intercept form, we can see that the slope, m2, is also -1/2.
Since the slopes of both lines are the same (-1/2), the lines are parallel.
To determine whether the lines represented by the given equations are parallel, perpendicular, or neither, we need to compare their slopes.
The given equations are:
1) y = -1/2x - 12
2) -6x - 12y = 21
Both equations are in a slope-intercept form (y = mx + c), where m represents the slope of the line.
For equation 1:
y = -1/2x - 12
Comparing this equation to the standard slope-intercept form (y = mx + c), we see that the slope (m) is -1/2.
For equation 2:
-6x - 12y = 21
To convert this equation into slope-intercept form, we isolate y on one side:
-12y = 6x + 21
Divide through by -12:
y = -(1/2)x - (7/2)
Comparing this equation to the standard slope-intercept form, we see that the slope (m) is -1/2.
As both equations have the same slope (-1/2) and the slopes are equal, the lines represented by these equations are parallel.
So, to summarize:
The lines represented by the equations y = -1/2x - 12 and -6x - 12y = 21 are parallel.