The slope intercept form of the equation of a line is given as:
y = mx + c
where m = the slope of the line
c = the y - intercept of the line
1) Two line are parallel if they have the same slope
That is:
[tex]\begin{gathered} \text{If the equation for line 1 is: y = m}_1x+c_1 \\ \text{If the equation for line 2 is: y = m}_2x+c_2 \\ \text{Then, line 1 is parallel to line 2 if m}_1=m_2 \end{gathered}[/tex]2) Two equations are perpendicular if the slope of one is the negative inverse of the other.
[tex]\text{That is : m}_1=\text{ }\frac{-1}{m_2}[/tex]3) Two equations are coincidental if they have the same slope and the same y intercept
[tex]\begin{gathered} \text{That is: m}_1=m_2_{} \\ \text{and c}_1=c_2 \end{gathered}[/tex]