the graph of which equation is parallel to the line that passes through (-1, 5), (4,7)

Question

Sthe graph of which equation is parallel to the line that passes through (-1, 5), (4,7)

Answer 1

(-1,5), (4,7)

a line through these 2 points has slope (7-5)/(4--1) = 2/5

y=mx +b where m=2/5

plug in either point to solve for b, the y intercept

7=(2/5)(4) + b

b = 7-8/5 = (35-8)/5 = 27/5

the line is y= 2x/5 + 27/5

any parallel will have the same slope, 2/5, but a different y intercept

most simple parallel line would be through the origin, with b=0

y=2x/5

y=2x/5 + any constant (except 27/5) is a parallel line. if the constant were 27/5, it wouldn't be parallel, because it would be the same line.

another way to find and graph a parallel line is add the same number to the y coordinates of the given two points (-1,5) and (4,7) to get (-1,5+c), (4,7+c)

such as (-1,6) and (4,8) where c=1. Plot those two points and connect them with a straight line. It's parallel to the line through (-1,5) and (4,7)