Parallel Lines How do you know two lines are parallel?

Determine if any of the sets of lines are parallel. Justify your answer.
Line a passes through (-2, 4) and (3, 14).
Line b passes through (7, 2) and (-1, 3).
Line c passes through (3, 1) and (0, -5).

Line a: y= -13x+4
Line b: 3x-y=7
Line c: 6x + 2y = 12

Write the equation of the line parallel to x+4y = 6 that passes through the point (4, -8).

How do you know two lines are parallel?:

if the lines were to continue forever they would NEVER EVER touch they would just go STRAIGHT like train tracks

a negative exponent is translated as follows:

so, we have

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for