I am going to give you pairs of line equations and your going to tell me if they are parrallel, perpendicular, neither, or the same line
9 answers
Sure, I can help with that. Please provide the pairs of line equations.
y+3x=1
6y+2x=-54
6y+2x=-54
To determine the relationship between the two lines represented by the equations y + 3x = 1 and 6y + 2x = -54, we need to compare the slopes of the lines.
We first need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope:
1. y + 3x = 1
y = -3x + 1
The slope of the first line is -3.
2. 6y + 2x = -54
6y = -2x - 54
y = -(1/3)x - 9
The slope of the second line is -(1/3).
The slopes are -3 and -(1/3), which are negative reciprocals of each other. When two lines have slopes that are negative reciprocals, they are perpendicular to each other.
Therefore, the lines represented by the equations y + 3x = 1 and 6y + 2x = -54 are perpendicular.
We first need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope:
1. y + 3x = 1
y = -3x + 1
The slope of the first line is -3.
2. 6y + 2x = -54
6y = -2x - 54
y = -(1/3)x - 9
The slope of the second line is -(1/3).
The slopes are -3 and -(1/3), which are negative reciprocals of each other. When two lines have slopes that are negative reciprocals, they are perpendicular to each other.
Therefore, the lines represented by the equations y + 3x = 1 and 6y + 2x = -54 are perpendicular.
y=-1/3x+5
4y+12x=4
4y+12x=4
To determine the relationship between the two lines represented by the equations y = -1/3x + 5 and 4y + 12x = 4, we need to compare the slopes of the lines.
We first need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope:
1. y = -1/3x + 5
The slope of the first line is -1/3.
2. 4y + 12x = 4
4y = -12x + 4
y = -3x + 1
The slope of the second line is -3.
The slopes are -1/3 and -3. These are not negative reciprocals nor the same value, so the lines are neither parallel nor perpendicular.
Therefore, the lines represented by the equations y = -1/3x + 5 and 4y + 12x = 4 are neither parallel nor perpendicular.
We first need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope:
1. y = -1/3x + 5
The slope of the first line is -1/3.
2. 4y + 12x = 4
4y = -12x + 4
y = -3x + 1
The slope of the second line is -3.
The slopes are -1/3 and -3. These are not negative reciprocals nor the same value, so the lines are neither parallel nor perpendicular.
Therefore, the lines represented by the equations y = -1/3x + 5 and 4y + 12x = 4 are neither parallel nor perpendicular.
2y+3x=−12
9y−6x=18
9y−6x=18
To determine the relationship between the two lines represented by the equations 2y + 3x = -12 and 9y - 6x = 18, we need to compare the slopes of the lines.
We first need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope:
1. 2y + 3x = -12
2y = -3x - 12
y = (-3/2)x - 6
The slope of the first line is -3/2.
2. 9y - 6x = 18
9y = 6x + 18
y = (6/9)x + 2
y = (2/3)x + 2
The slope of the second line is 2/3.
The slopes are -3/2 and 2/3. These are not negative reciprocals nor the same value, so the lines are neither parallel nor perpendicular.
Therefore, the lines represented by the equations 2y + 3x = -12 and 9y - 6x = 18 are neither parallel nor perpendicular.
We first need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope:
1. 2y + 3x = -12
2y = -3x - 12
y = (-3/2)x - 6
The slope of the first line is -3/2.
2. 9y - 6x = 18
9y = 6x + 18
y = (6/9)x + 2
y = (2/3)x + 2
The slope of the second line is 2/3.
The slopes are -3/2 and 2/3. These are not negative reciprocals nor the same value, so the lines are neither parallel nor perpendicular.
Therefore, the lines represented by the equations 2y + 3x = -12 and 9y - 6x = 18 are neither parallel nor perpendicular.
wrong
Apologies for the error. Let's correct that:
1. 2y + 3x = -12
2y = -3x - 12
y = (-3/2)x - 6
2. 9y - 6x = 18
9y = 6x + 18
y = (6/9)x + 2
y = (2/3)x + 2
Comparing the slopes:
First line: m1 = -3/2
Second line: m2 = 2/3
The product of the slopes is (-3/2)*(2/3) = -1, which means that the lines are perpendicular to each other.
Therefore, the lines represented by the equations 2y + 3x = -12 and 9y - 6x = 18 are perpendicular.
1. 2y + 3x = -12
2y = -3x - 12
y = (-3/2)x - 6
2. 9y - 6x = 18
9y = 6x + 18
y = (6/9)x + 2
y = (2/3)x + 2
Comparing the slopes:
First line: m1 = -3/2
Second line: m2 = 2/3
The product of the slopes is (-3/2)*(2/3) = -1, which means that the lines are perpendicular to each other.
Therefore, the lines represented by the equations 2y + 3x = -12 and 9y - 6x = 18 are perpendicular.
7 answers