Tell whether the lines for each pair of equation are parallel, perpendicular or neither y=-1/6x-5 24x-4y=12
To determine whether the lines described by each pair of equations are parallel, perpendicular, or neither, we need to compare their slopes.
The first equation, y = -1/6x - 5, is in slope-intercept form, where the slope is the coefficient of x (-1/6 in this case).
The second equation, 24x - 4y = 12, needs to be rearranged into slope-intercept form.
24x - 4y = 12
-4y = -24x + 12
y = 6x - 3
In this second equation, the coefficient of x is 6.
Since the slopes of the lines -1/6 and 6 are negative reciprocals of each other (their product is -1), the lines are perpendicular.
To determine whether the lines represented by each pair of equations are parallel, perpendicular, or neither, we need to examine their slopes.
The given equations are:
1. y = -1/6x - 5 (Equation 1)
2. 24x - 4y = 12 (Equation 2)
First, let's rewrite Equation 2 in slope-intercept form (y = mx + b):
2. 24x - 4y = 12
-4y = -24x + 12
y = 6x - 3 (Equation 3)
Now, we can compare the slopes of Equation 1 and Equation 3. The slope-intercept form of the equations is:
1. y = (-1/6)x - 5
2. y = 6x - 3
The slopes are:
Equation 1: -1/6
Equation 3: 6
Since the slopes are negative reciprocals of each other, these lines are perpendicular.
To determine whether the lines are parallel, perpendicular, or neither, we can compare their slopes. The slope of a line can be found by looking at the coefficient of x in the equation when it is in slope-intercept form (y = mx + b).
First, let's write both equations in slope-intercept form:
1. y = -1/6x - 5
To find the slope, we can compare this equation to y = mx + b. In this case, m = -1/6. So, the slope of this line is -1/6.
2. 24x - 4y = 12
To write this equation in slope-intercept form, we need to isolate y. Start by subtracting 24x from both sides:
-4y = -24x + 12
Next, divide by -4 to solve for y:
y = 6x - 3
Now, we can compare this equation to y = mx + b. In this case, m = 6. So, the slope of this line is 6.
Since the slopes of the two lines are -1/6 and 6, which are negative reciprocals of each other (their product is -1), these lines will be perpendicular to each other.