Question 283338
Theo did a great job explaining the problem.
However he is a little off on his conclusion.
"The equations that were multiples of each other in standard form BECOME (my caps) the same as each other in slope-intercept form."

They CAN become the same .
y = (-10/14)x + (70/14)
CAN become 
y = (-5/7)x + (35/7)
y = (-10/14)x + (70/14) DOES NOT HAVE TO change.
Also one might be in decimal form such as .5 and the other might be a fraction such as 1/2