Describing parallel lines?

Question

Writes the equation of the line parallel to the given line and passing through the given point.

1) y= x + 4; (2,5)
2) y= 3x - 1; (1,4)
3) y= 2x - 2; (2,8)
4) y= x - 7; (4,6)
5) y= 3x - 3; (-2,-5)

Answer 1

Well since parallel lines have the same slope you have a starting point for each question. Simple use the form y=mx+b and plug in the slope of the original line for m and the order pair (x, y) and solve for b.

y=x+4 m=1 5=(1)(2)+b b=3 so y=x+3

y=3x-1 m=3 4=(3)(1)+b b=1 so y=3x+1

y=2x-2 m=2 8=(2)(2)+b b=4 so y=2x+4

y=x-7 m=1 6=(1)(4)+b b=2 so y=x+2

y=3x-3 m=3 -5=(3)(-2)+b b=0 so y=3x

Answer 2

a million) 6y = 3x - 12; (2, -4) y = 3x/6 - 2 y = (a million/2)x - 2. as a result, m = a million/2 (it is the slope) In Analytic Geometry, 2 lines are parallel if their slopes are equivalent. employing the coordinates: x1 = 2, y1 = -4 and the equation: m = [y - y1]/[x - x1] a million/2 = [y - (-4)]/[x - 2] 2{a million/2} = 2{[y + 4]/[x - 2]} a million = 2(y + 4)/(x - 2) a million = (2y + 8)/(x - 2) a million(x - 2) = 2y + 8 x - 2 = 2y + 8 x - 2y - 2 - 8 = 0 x - 2y - 10 = 0 answer. 2) (a million/2)y = 3x; (-2, - 9) 2(a million/2)y = 2(3x) y = 6x . as a result, 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 + a million. as a result, 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; (a million, -3) y = -20x/10 - 20/10 y = -2x - 2. as a result, m = -2 and x1 = a million, y1 = -3 m = [y - y1]/[x - x1] -2 = [y - (-3)]/[x - a million] -2 = [y + 3]/[x - a million] -2[x - a million] = [y + 3] -2x + 2 = y + 3 -2x - y + 2 - 3 = 0 -2x - y - a million = 0 or -a million(-2x - y - a million) = -a million(0) 2x + y + a million = 0 answer. 5) 3x = 3y - 12; (-5, -eleven) 3y - 12 = 3x 3y = 3x + 12 y = 3x/3 + 12/3 y = x + 4. as a result, m = a million and x1 = -5, y1 = -eleven m = [y - y1]/[x - x1] a million = [y -(-eleven)]/[x -(-5)] a million[x + 5] = y + eleven x + 5 = y + eleven x - y + 5 - eleven = 0 x - y - 6 = 0 I unquestionably have a feeling it is an task. Why do no longer you bypass over them and notice in case you recognize the answer. basically copying the answer won't help you. you're able to be attentive to the way each and every is solved. desire to help. teddyboy

Answer 3

Parallel lines have the same slope. In order to fins lines parallel to those given in the equation and passing through the given point, you replace the coordinate pair (x,y) with the x and y in the equation and solve for b. For example:

1. y=x+2 (2,5)
-since it is a linear equation, it is in the form y=mx+b (m being slope, b being y-intercept)
-substitute the coordinate pair - ex. 5=2+b
-solve for b
-b= 3
So the equation parallel to the original and passing through that point is y=x+3

2. y=3x-1 (1,4)
4=3(1)+b
B=1

Parallel line - y=3x+1

3. Y=2x-2 (2,8)
8=2(2) +b
B=4
Parallel line- y=2x+4


4. y=x-7 (4,6)
6=4+b
B=2
Parallel- y=x+2

5. y=3x-3 (-2,-5)
-5=3(-2)+b
-5=-6+b
B=1
Parallel line- y=3x+1

Answer 4

1. y = x + 3
2. y = 3x + 1
3. y = 2x + 4
4. y = x + 2
5. y = 3x + 1

Answer 5

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