How do you know if an equation is parallell or perpendicular or neither?

Answer 1

you can check if two equations are parallel, perpendicular or neither by comparing their slopes. If the slope of one linear equation is identical to the other or is a multiple of it then they are either parallel or perpendicular.

ex. Slope of line "A" is 4/3

Slope of line "B" is 8/6

because slope B is equal to 4 times slope A they are parallel. This is whats known as a scalar multiple. it just means that they both head in the exact same direction even though one is a little bit larger than the other one.

Also note that if two equations do have similar or equal slopes, you must also check to see if they are identical lines (coincide) or if they are lines that are parallel but never touch each other (parallel and distinct). To do this, take any point that contains both and X and Y variable that is not 0 from one equation and input it into the other equation. See if the Y you put into the equation is what you get when you calculate the x side of the formula.

Ex. (Line "A") y=m(x)+b

(Line "B") y=m(x)+b

if line A is Y=4/3(x)+1 then set x to any non zero value and solve for it

y=4/3(3)+1=5 thus, one point on line A is (3,5)

now put this point into Line"B" and see if the left hand side is equal to the right hand side (LHS=RHS)

Line"B" y=m(x)+b

if line B is y=8/6(x)+1 then when you input the values from Line A you get

5=8/6(3)+1

LHS=5

RHS=5

They are equal, this means that this point exists on this line. Thus both lines are on top of each other or more noticeably. Both equations represent the same line.

To calculate if the lines are perpendicular you also compare the slopes of both lines. If one line is perpendicular to the other then their slopes will be negative inverses of one another. In lament terms, they are as follows.

Slope "C" = 7/4 Slope "D" = -4/7

The line of "C" is perpendicular to the line of "D"

the slopes must have their fractions inverted (flipped upside down) and their sign must be also switched from either positive to negative or from negative to positive.