Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
Y=-1/6x-5
24x-4y=12
To determine whether these lines are parallel, perpendicular, or neither, we can compare their slopes.
For the first equation, y = -1/6x - 5, the slope is -1/6.
To find the slope of the second equation, 24x - 4y = 12, we need to rewrite it in slope-intercept form (y = mx + b).
Rearranging the equation by isolating the y-term, we get -4y = -24x + 12. Dividing both sides by -4, we obtain y = 6x - 3.
The slope of the second equation is 6.
Since the slopes of the two equations are different (one is -1/6 and the other is 6), the lines are neither parallel nor perpendicular.
To determine whether the lines for the pair of equations are parallel, perpendicular, or neither, we can compare their slopes.
The given equations are:
1) Y = -1/6x - 5
2) 24x - 4y = 12
To determine the slope of the first equation, we can rewrite it in the form y = mx + b, where m is the slope. Comparing the equation with this form, we can see that the slope is -1/6.
To find the slope of the second equation, we'll rearrange it into slope-intercept form:
24x - 4y = 12
-4y = -24x + 12
Divide both sides by -4:
y = 6x - 3
Comparing this equation with the slope-intercept form, we can see that the slope is 6.
Now, we can compare the slopes:
The slope of the first equation is -1/6 and the slope of the second equation is 6.
Two lines are parallel if their slopes are equal. However, -1/6 is not equal to 6, so the lines are not parallel.
Two lines are perpendicular if the product of their slopes is -1. Let's check if this condition is satisfied:
(-1/6) * 6 = -1
As -1 is the product of the slopes, the lines are perpendicular.
Therefore, the lines represented by the given pair of equations are perpendicular.
To determine whether the lines described by the given equations are parallel, perpendicular, or neither, we need to examine the slopes of the lines.
The general form of a linear equation is y = mx + b, where m represents the slope of the line.
For the first equation, y = -(1/6)x - 5, we can identify the slope by comparing it to the general form. In this case, the slope is -(1/6).
For the second equation, 24x - 4y = 12, we need to rearrange it to the slope-intercept form (y = mx + b) to find the slope.
Start by isolating y by subtracting 24x from both sides:
-4y = -24x + 12
Next, divide through by -4 to find the slope:
y = (24/4)x - 3
y = 6x - 3
Comparing this equation to the general form, we find that the slope is 6.
Now that we have the slopes, we can determine the relationship between the lines:
If the slopes are equal, the lines are parallel.
If the slopes are negative reciprocals (one is the negative inverse of the other), the lines are perpendicular.
If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
In this case, the slope of the first equation is -(1/6), and the slope of the second equation is 6.
Since the slopes are negative reciprocals (one is the negative inverse of the other), the lines are perpendicular.
Therefore, the lines described by the given equations are perpendicular.