Tell wether the lines for each pair of equation are parallel, perpendicular or neither
y=-1/6x-5
24x-4y=12
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines.
For the first equation, y = -1/6x - 5, we can identify the slope by comparing this equation to the standard slope-intercept form, y = mx + b. Here, the slope (m) is -1/6.
For the second equation, 24x - 4y = 12, we need to rewrite it in slope-intercept form. Let's isolate y:
-4y = -24x + 12
y = 6x - 3
Comparing this equation to the standard form, we can see that the slope (m) is 6.
Since the slopes of the two equations are not the same and they are also not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
To determine if the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
The given equations are:
1) y = (-1/6)x - 5
2) 24x - 4y = 12
We need both equations to be in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange equation 2 into slope-intercept form:
24x - 4y = 12
-4y = -24x + 12
Divide by -4:
y = 6x - 3
Now we can compare the slopes of the two equations:
1) The slope of y = (-1/6)x - 5 is -1/6.
2) The slope of y = 6x - 3 is 6.
Since the slopes are negative reciprocals of each other, -1/6 and 6, the lines are perpendicular to each other.
To determine whether the lines represented by the pair of equations are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a linear equation can be written as y = mx + b, where m represents the slope of the line.
Let's start by writing the equations in slope-intercept form:
Equation 1: y = (-1/6)x - 5
Equation 2: 24x - 4y = 12
To convert Equation 2 into slope-intercept form, we need to isolate y:
24x - 4y = 12
-4y = -24x + 12
y = (1/4)x - 3
Now we can compare the slopes of the two equations. The coefficient of x in Equation 1 represents the slope, which is -1/6, and the coefficient of x in Equation 2 represents the slope, which is 1/4.
If the slopes of two lines are equal, then the lines are parallel. If the slopes are negative reciprocals of each other (i.e., multiplying one slope by -1 gives the other slope), then the lines are perpendicular. Otherwise, if the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
Let's compare the slopes:
Slope of Equation 1: -1/6
Slope of Equation 2: 1/4
The slopes -1/6 and 1/4 are not equal, and their product (-1/6)*(1/4) = -1/24 is not -1. Therefore, the lines represented by the pair of equations are neither parallel nor perpendicular.