Determine if the lines 4x + y = 6 and -3x + 3y = -6 are parallel, perpendicular, or neither.?
回答 (5)
2016-08-03 12:31 am
✔ 最佳答案
We must put both equations of the form y = mx + b. If the slopes (or m) are equal, then the lines are parallel. If they are the same number, but one is negative, the lines are perpendicular. If the m values are not equal in any way, then neither are true.4x + y = 6
y = -4x + 6, so m = -4
-3x + 3y = -6
3y = 3x - 6
y = x - 2, so m = 1
The lines are neither parallel nor perpendicular.
2016-08-02 9:33 pm
Slope of the line (4x + y = 6), m₁
= -4/1
= -4
Slope of the line (-3x + 3y = -6), m₂
= -(-3/3)
= 1
m₁ ≠ m₂ and m₁m₂ ≠ -1
The two lines are neither parallel nor perpendicular.
= -4/1
= -4
Slope of the line (-3x + 3y = -6), m₂
= -(-3/3)
= 1
m₁ ≠ m₂ and m₁m₂ ≠ -1
The two lines are neither parallel nor perpendicular.
2016-08-02 9:44 pm
We shall transform the eqn for each line into slope y-intercept form to make
comparisons easy. 4x+y = 6, ie., y = -4x+6..[1]. -3x+3y = -6, ie., y =x -2..[2].
Slope of line in ([1] , [2]) = (-4 , 1). Clearly lines [1] & [2] are neither parallel
nor perpendicular since m1 not = m2 or -1/m2, where m1 = slope line [1] &
m2 = slope line [2].
comparisons easy. 4x+y = 6, ie., y = -4x+6..[1]. -3x+3y = -6, ie., y =x -2..[2].
Slope of line in ([1] , [2]) = (-4 , 1). Clearly lines [1] & [2] are neither parallel
nor perpendicular since m1 not = m2 or -1/m2, where m1 = slope line [1] &
m2 = slope line [2].
2016-08-02 9:32 pm
4x + y = 6
y = -4x + 6 which has a slope of -4
-3x + 3y = -6
3y = 3x - 6
y = x - 2 which has a slope of 1
-4 and 1 are not equal so the lines are parallel.
-4 and 1 are not negative reciprocals of each other so the lines are not perpendicular.
The answer is neither.
y = -4x + 6 which has a slope of -4
-3x + 3y = -6
3y = 3x - 6
y = x - 2 which has a slope of 1
-4 and 1 are not equal so the lines are parallel.
-4 and 1 are not negative reciprocals of each other so the lines are not perpendicular.
The answer is neither.
2016-08-02 9:31 pm
No
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