Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1.
Solve for x. 3x – 2y = 6
Can anyone help me with these 3 problems please?
2007-09-21 16:05:07 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
y=mx+b where b is the the y intercept, and m is the slope.
so on the first problem:
You are given m=6
y=6x+b then you can plug your equation in and solve for b:
6=12+b
b=-6
so the equation is:
y=6x-6
The second problem:
The slope of parallel lines are the same. The slope of perpendicular lines are a negative reciprical (not sure on the spelling) of each other...which is to say if the slope is 2 on one line, a perpendicular line would have a slope of -1/2
So you have a slope of -3 therefore a perpendicular line would have a slope of 1/3.
and a y intercept of 5.
So m = 1/3 and b=5
y=1/3 x +5
The last one...just isolate x on one side of the equal sign
3x-2y=6
3x-2y+2y=6+2y
3x=6+2y
3x/3=(6+2y)/3
x=6/3+2y/3
x=2+2/3 y (with the y being on top)
2007-09-21 16:15:41 · answer #1 · answered by Patty C 3 · 1⤊ 0⤋
Use the slope-intercept form of a line to do the first 2 problems:
y = mx + b, where m is the slope and b is the y-intercept.
1)
6 = 6 * 2 + b
6 = 12 + b
b = -6
y = 6x - 6
2) For the line y = -3x +1, the slope m = -3, so the slope perpendicular to this is 1/3 (negative inverse)
y = 1/3 x + b
5 = (1/3)(0) + b
b = 5
y = 1/3 x + 5
3)
3x - 2y = 6
3x = 2y + 6
x = (2y + 6)/3
x = 2/3 y + 2
2007-09-21 16:14:12 · answer #2 · answered by N E 7 · 0⤊ 0⤋
y = mx + b, m = slope b = y - intercept
y = 6x +b, to find the y-intercept plug in the given point and solve for b
6 = 6(2) + b
6 = 12 + b
-6 = b
equation: y = 6x - 6
The next example, (0, 5) is the y - intercept so we have y = mx + 5
The slope is perpendicular to y = -3x + 1. The slope here is -3, a line perpendicular to this would be the negative reciprocal or 1/3
so the equation is: y = 1/3x + 5
solve for x:
3x - 2y = 6, add 2y
3x = 2y + 6, divide by 3
x = 2/3x + 2
2007-09-21 16:10:00 · answer #3 · answered by sfroggy5 6 · 2⤊ 0⤋
1. 6=6(2)+b
6=12+b
b=-6
THe equation is y=6x-6
2. 5=1/3(0)+b
y=1/3x+5
3. 3x=2y+6
x=2/3y+2
2007-09-21 16:11:35 · answer #4 · answered by asphyxia 3 · 1⤊ 0⤋
y = mx +b
6=6(2)+b
-6 = b
ans. y = 6x - 6 Check: 6 = 6(2) -6
perpendicular slope to m is -1/m
y=x / 3 +5
y= mx + b
Rearranging,
-2y = -3x +6
y = 3/2x -3; Now take y = 0:
0 = 3/2x - 3
3 = 3/2x
x = 2.
2007-09-21 16:28:20 · answer #5 · answered by Anonymous · 1⤊ 0⤋
1)using point slope form
y-6=6(x-2)
y-6=6x-12
6x-y-6=0
2)in equation y=-3x+1
slope is -3 if perpendicular it is the - reciprocal and that is 1/3
using slope intercept form
y=1/3x +5
3)3x-2y=6
3x=2y+6
x=2y/3 +2
2007-09-21 16:14:35 · answer #6 · answered by ijoeboy_05 2 · 1⤊ 0⤋
Question 1
y - 6 = 6 (x - 2)
y = 6x - 6
Question 2
y = (1/3) x + 5
Question 3
3x = 6 + 2y
x = 2 + (2/3) y
2007-09-22 04:28:33 · answer #7 · answered by Como 7 · 3⤊ 0⤋