may i please get soem help on a math question?

Question

how do you write two equations that represent parallel lines? also how do u write equation representing a perpendicular line?

Answer 1

Parallel lines (same slopes)
y = mx + b
y = mx + c

For example:
y = 3x + 2
y = 3x + 5

Perpendicular lines (slopes are negative reciprocals)
y = mx + b
y = (-1/m)x + c

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

Answer 2

For two parallel lines, coefficients of x and y are the same, the constant may or may not be the same.

eg

2x+3y=4

2x+3y=9

For the equation of a line perpendicular to another line, interchange coefficients of x and y and negate the coeffitcient of y after interchanging, and introduce some constant.

eg:

for 2x-3y=6, perpendicular line is of the form,

-3x-2y=k

value of k can be found by substituting any point like (1,2) that lies on the perpendicular line.

:)

Answer 3

2 equations w/ a parallel lines will ALWAYS have the same slope

2 equations w/ perpendicular lines will ALWAYS have slopes, when multiplied, will be the negative reciprocal

e.g. y = -4x - 5 and y = -4x+8
the slope (m) is -4
the slopes are the same
the lines are parallel

e.g. y = -4x - 5 and y = 1/4x +8
the slope (m) is -4 x -1= 4 and find the reciprocal
which is 1/4

Answer 4

The equation for a line has the form of:

y=mx + b

if two lines are parallel, then the m terms for both lines will be identical, but the b terms will be different.

so the following lines are parallel,

y =3 x + 4
y= 3x - 4
y= 3x

Answer 5

parallel line equations have the same slope such as y=3x+2 and y=3x-9
Perpendicular lines have slopes that are the inverse and opposite signs such as y=4x+2 and y=-1/4x+10

Answer 6

for parallel, write an equation then place || inbetween
for perp, place a + inbetween