Tell whether the lines for each pair of equation are parallel perpendicular or neither.
Y=-1/2x-12
-6x-12y=21
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
For the first equation, y = -1/2x - 12, we can see that the coefficient of x is -1/2, which represents the slope of the line.
For the second equation, -6x - 12y = 21, let's rearrange it into slope-intercept form (y = mx + b):
-12y = 6x + 21
Dividing both sides by -12, we get:
y = -1/2x - 7/4
Now we can compare the slopes:
The slope of the first equation is -1/2.
The slope of the second equation is also -1/2.
Since the slopes of the two lines are equal, the lines are parallel.
To determine if two lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines.
Let's rewrite the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Equation 1: y = -1/2x - 12
Equation 2: -6x - 12y = 21
To convert Equation 2 into slope-intercept form, we need to isolate y. Let's solve for y:
-6x - 12y = 21
-12y = 6x + 21
Divide both sides by -12:
y = -1/2x - 7/4
Comparing the two equations, we can see that both lines have a slope of -1/2. Since the slopes are the same, the lines are parallel.
Therefore, the lines described by the equations y = -1/2x - 12 and y = -1/2x - 7/4 are parallel.
To determine whether the lines given by the pair of equations are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line. For the first equation, y = (-1/2)x - 12, the slope (m) is -1/2.
To compare the slopes, we need to rewrite the second equation, -6x - 12y = 21, in the slope-intercept form. Let's solve this equation for y:
-6x - 12y = 21
Divide both sides by -12:
-6x/(-12) - 12y/(-12) = 21/(-12)
Simplify:
1/2x + y = -7/4
Rearranging to slope-intercept form:
y = -1/2x - 7/4
The second equation, y = -1/2x - 7/4, also has a slope (m) of -1/2.
Comparing the slopes, we observe that both equations have the same slope (-1/2). When two lines have the same slope, they are parallel. Therefore, the lines represented by the given pair of equations are parallel.