Question

Explain, in complete sentences, the relationship between the equations of parallel lines

Answer 1

They will have the same slope but different y-intercepts.

Answer 2

For any two lines that are parallel, their slopes will be same, but the value of the y-intercept will be different.



So basically ifa line is "ax+by+c=0"'
its parallel twin will be "ax+by+k=0"



Its parallel twin may also be written in a form "px+qy+r=0"
where,
\[\frac a p = \frac b q \neq \frac c r\]

If the ratio a:p = c=r, then the lines would be coincident - that is both equations would represent one and the same line.