Consider the line . What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Answer 1

To be parallel the line has to have the same slope

the slope = the coefficient of the x term when the equation is solved for y

y=mx + b has slope = m

a parallel line will also have slope = m

y=mx + a, where a does not equal b. If a=b they are not parallel, but they are the same line

a perpendicular line will have slope that is the negative inverse

y=(-1/m)x + b where b is any number

For example: 2x + y = 4, solve for y

y=-2x +4. -2 is the slope

a parallel line is y=-2x + 5 or + any number except 4

a perpendicular line is y=(1/2)x + 10 or any number, including 4