shanya graphed the line represented by the equation y = x - 6
write an equation for the line that is parallel to the given line.
write an equation for a line that is perpendicular to the given line
Write and equation for the line that is identical to the given line but has different coefficients.
thanks!! please show work
2006-11-26 08:42:53 · 4 answers · asked by Fuzzyglasses 3 in Education & Reference ➔ Homework Help
Parallel has the same slope, different intercept
y=x+6 for example
Perpendicular has the negative inverse slope
y=-x+6 for example
idential is just multiplying a constant by both sides of the equation:
2y=2x-12 for example
j
2006-11-26 08:48:29 · answer #1 · answered by odu83 7 · 1⤊ 0⤋
Here is a parallel equation: y=x
Basically, any two lines with the same slope but different intercepts are parallel.
Perpendicular
y= -x - 6
The slope of a perpendicular line is the negative reciprocal. So slope is:
-(1/1) = -1
Identical line different coefficients:
Just multiply the whole line by two
2*y=2*(x-6)
2y=2x-12
2y= 2x - 12
2006-11-26 16:52:20 · answer #2 · answered by morris181340 2 · 0⤊ 0⤋
equation of a line is y = m*x +c
parallel lines have same slope, but their intercepts will be different.
so parallel lines are y = m*x + (c1), y = m*x + (c2),etc
in your line, c = -6, m = 1.. so parallel lines are ...
y = x-5, y=x-4, y=x-3, y=x-2.....
perpendicular lines are those whose slope are at a value pie/2 to each other.. we know, tan( x+ (pie/2)) is - cot (x)...(note the minus), and cot(x) is 1/tan(x).so perpendicular lines have slopes that are negative reciprocals of each other....
so perpendicular line for your line is y = (-1/1)*x -6....
(i've shown the negative reciprocal of 1...lol, but if it had been 2..that is y =2*x-6, you would have got for perpendicular line, the slope as y = (-1/2)*x -6...get it?)
identical line is just a line with coefficients that are a multiple of the original...
so ...a*y = a*m*x - (6*a)....are identical lines to your line...
a can be any rational number you choose, except 0..a = -3,-2,-1, 1, 2,3 ...etc
2006-11-26 17:21:26 · answer #3 · answered by amateur_astrologer 2 · 0⤊ 0⤋
parallel: same slope; different y-intercept y=x-5
perp.: opposite reciprocal slope; any y-intercept y=-1x-6
same: just multiply by two 2y=2x-12 divide by 2 and it gives you your original equation.
2006-11-26 16:50:06 · answer #4 · answered by x0xDrumMajorx0x 2 · 0⤊ 0⤋