Find the equation of the line parallel to f(x) = -2x + 6 that goes through the p

Question

Find the equation of the line parallel to f(x) = -2x + 6 that goes through the point (-6, 4). Find the equation of the line perpendicular to f(x) = -2x + 6 that goes through the point (-6, 4). Identify the following pairs of lines as parallel, perpendicular, or neither. Circle your answer. y = 3x + 1 and y = - 1/3 x + 1 parallel perpendicular neither y = - 1/2 x - 2 and y = 1/2 x + 1 parallel perpendicular neither y = -6x + 2 and y = -6x - 3 parallel perpendicular neither y - 3 = 2(x + 3) and y - 4 = 2(x - 1) parallel perpendicular neither y + 2 = 6(x - 3) and y - 4 - 2(x - 3) parallel perpendicular neither y = -10x + 50 and y = 10x - 50 parallel perpendicular neither 2x - 6y = 12 and 3x + y = 1 parallel perpendicular neither -1.5x + 3y = 0 and 3x - 6y = 2 parallel perpendicular neither

Explanation / Answer

9 ) Given that

f(x) = -2x + 6 , (-6,4)

Let y = -2x + 6

The given line is in the form of y = mx + b

m = slope

If two lines are said to be parallel then their slopes are equal

i.e m1 = m2

Slope of given line m1 = -2

Hence ,

Slope of second line m2 = -2 [ slope for parallel lines re equal ]

Let (x1 , y1) = (-6 , 4)

The equation of line is ,

y - y1 = m(x - x1 )

y - 4 = -2(x - (-6) )

y - 4 = -2(x + 6)

y -4 = -2x - 12

y = -2x - 12 + 4

y = -2x - 8

Therefore ,

The equation of line parallel to given line is , y = -2x - 8

10 ) Given that

If two lines are said to be perpendicular then their product equal to -1

i.e m1.m2 = -1

Slope of line f(x) = -2x + 6 is m1 = -2

-2.m2 = -1

2m2 = 1

m2 = 1/2

Slope of second line is m2 = 1/2

Let (x1 , y1) = (-6 , 4)

The equation of line is ,

y - y1 = m(x - x1 )

y - 4 = (1/2) (x -(-6) )

y -4 = (1/2) (x + 6)

y - 4 = (1/2) x + 3

y = (1/2)x + 7

Therefore ,

The equation of line perpendicular to given line is ,

  y = (1/2)x + 7

11 )

a ) y = 3x + 1 and y = (-1/3)x + 1

Slope of first line m1 = 3

Slope of second line m2 = (-1/3)

m1.m2 = 3.(-1/3)

m1.m2 = -1

Hence ,

The given two lines are perpendicular

b ) y = (-1/2)x - 2 and y = (1/2)x + 1

Slope of first line m1 = (-1/2)

Slope of second line m2 = (1/2)

m1.m2 =   (-1/2).(1/2) = -1

Hence ,

The given two lines are perpendicular

c ) y = -6x + 2 and y = -6x - 3

Slope of first line m1 = -6

Slope of second line m2 = -6

Slopes of two lines are equal

Hence ,

The given two lines are parallel

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