Describing parallel lines?

Question

Rewrite each equation in the form y= mx + b. Then write an equation for a line parallel to the first and passing through the given point.


1) 6y = 3x - 12; (2,-4)
2) 1/2y = 3x; (-2,-9)
3) 5y = 4x + 5; (-5,-4)
4) 10y = -20x -20; (1,-3)
5) 3x = 3y - 12; (-5,-11)

Answer 1

Hi,

1) 6y = 3x - 12; (2,-4)
y = ½x - 2
m = ½ so a parallel line also has a slope of ½

Using m = ½ and (2,-4) in y = mx + b

y = mx + b
-4 = ½(2) + b
-4 = 1 + b
-5 = b

y = ½x - 5 is the parallel line.


2) 1/2y = 3x; (-2,-9)
y = 6x
m = 6 so a parallel line also has a slope of 6

Using m = 6 and (-2,-9) in y = mx + b

y = mx + b
-9 = 6(-2) + b
-9 = -12 + b
3 = b

y = 6x + 3 is the parallel line.


3) 5y = 4x + 5; (-5,-4)
y = 4/5x + 1
m = 4/5 so a parallel line also has a slope of 4/5

Using m = 4/5 and (-5,-4) in y = mx + b

y = mx + b
-4 = 4/5(-5) + b
-4 = -4 + b
0 = b

y = 4/5x is the parallel line.

4) 10y = -20x -20; (1,-3)
y = -2x - 2
m = -2 so a parallel line also has a slope of -2

Using m = -2 and (1,-3) in y = mx + b

y = mx + b
-3 =-2(1) + b
-3 = -2 + b
-1 = b

y = -2x - 1 is the parallel line.


5) 3x = 3y - 12; (-5,-11)
y = x + 4
m = 1 so a parallel line also has a slope of 1

Using m = 1 and (-5,-11) in y = mx + b

y = mx + b
-11 = 1(-5) + b
-11 = -5 + b
-6 = b

y = x - 6 is the parallel line.


I hope that helps!! :-)

Answer 2

1) 6y = 3x - 12; (2, -4)
y = 3x/6 - 2
y = (1/2)x - 2. Therefore, m = 1/2 (this is the slope)
In Analytic Geometry, two lines are parallel if their slopes
are equal. Using the coordinates: x1 = 2, y1 = -4
and the equation:
m = [y - y1]/[x - x1]
1/2 = [y - (-4)]/[x - 2]
2{1/2} = 2{[y + 4]/[x - 2]}
1 = 2(y + 4)/(x - 2)
1 = (2y + 8)/(x - 2)
1(x - 2) = 2y + 8
x - 2 = 2y + 8
x - 2y - 2 - 8 = 0
x - 2y - 10 = 0 answer.

2) (1/2)y = 3x; (-2, - 9)
2(1/2)y = 2(3x)
y = 6x . Therefore, m = 6. With x1 = -2, and
y1 = -9
m = [y - y1]/[x - x1]
6 = [y - (-9)]/[x - (-2)]
6 = (y + 9)/(x + 2)
6(x + 2) = (y + 9)
6x + 12 = y + 9
6x - y + 12 - 9 = 0
6x - y - 3 = 0 Anwer.

3) 5y = 4x + 5; (-5, -4)
y = 4x/5 + 5/5
y = (4/5)x + 1. Hence, m = 4/5. x1 = -5, y1 = -4
m = [y - y1]/[x - x1]
4/5 = [y -(-4)]/[x - (-5)]
4/5(x + 5) = (y + 4
5[4/5(x + 5)] = 5(y + 4)
4(x + 5) = 5y + 20
4x + 20 = 5y + 20
4x - 5y + 20 - 20 = 0
4x - 5y = 0 Answer.

4) 10y = -20x - 20; (1, -3)
y = -20x/10 - 20/10
y = -2x - 2. Hence, m = -2 and x1 = 1, y1 = -3

m = [y - y1]/[x - x1]
-2 = [y - (-3)]/[x - 1]
-2 = [y + 3]/[x - 1]
-2[x - 1] = [y + 3]
-2x + 2 = y + 3
-2x - y + 2 - 3 = 0
-2x - y - 1 = 0 or
-1(-2x - y - 1) = -1(0)
2x + y + 1 = 0 answer.

5) 3x = 3y - 12; (-5, -11)
3y - 12 = 3x
3y = 3x + 12
y = 3x/3 + 12/3
y = x + 4. Hence, m = 1 and x1 = -5, y1 = -11

m = [y - y1]/[x - x1]
1 = [y -(-11)]/[x -(-5)]
1[x + 5] = y + 11
x + 5 = y + 11
x - y + 5 - 11 = 0
x - y - 6 = 0

I have a feeling this is an assignment. Why don't you go over them and see if you understand the solution. Merely copying the solution won't help you. You have to understand how each is solved.

Hope to help.


teddyboy

Answer 3

Parallel lines have the same slope, m.
1), 3), 4) Divide by the coefficient of y. Then use the point-slope form of a linear equation: y - y1 = m(x - x1). Using the value of m of the given equations & points.
2) (1/2)y = 3x; (-2, 9)
y = 6x, m = 6.
y - 9 = 6(x + 2)
y = 6x + 12 + 9
y = 6x + 21.

5) 3x = 3y - 12
x = y - 4
x + 4 = y
y = x + 4, m = 1.

Answer 4

1) 6y = 3x - 12; (2,-4)
y= (1/2)x-2 m=(1/2)
-4=(1/2)(2)+b gives a b (y-intercept) of -5
parallel line is y = (1/2)x-5

2) 1/2y = 3x; (-2,-9)
y= 2x m = 2
-9=2(-2)+b gives a b (y-intercept) of -5
parallel line is y = 2x-5


3) 5y = 4x + 5; (-5,-4)
y= (4/5)x+1 m = 4/5
-4=(4/5)(-5)+b gives a b (y-intercept) of 0
parallel line is y = (4/5)x+0


4) 10y = -20x -20; (1,-3)
y= -2x-2 m =- 2
-3=-2(1)+b gives a b (y-intercept) of -1
parallel line is y = -2x-1


5) 3x = 3y - 12; (-5,-11)
3y= 3x+12
y=1x+4 m =1
-11=1(-5)+b gives a b (y-intercept) of -6
parallel line is y = 1x-6

Answer 5

1. y = 1/2 x -2 ; y = 1/2 x - 6
2. y = 6x ; y = 6x + 3
3. y = 4/5 x + 1 ; y = 4/5 x
4. y = -2x -2 ; y = -2x - 1
5. y = x + 4 ; y = x - 6

Answer 6

there are at least 3 examples of this in your book before you get to the exercises for that section.

read them, do them while you are reading them and then the above problems will be easy.