Question

How do you find out if a like is parallel, perpendicular, or coincidental when theres 2 equations

Answer 1

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:

`\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}`

2) Two equations are perpendicular if the slope of one is the negative inverse of the other.

`\text{That is : m}_1=\text{ }(-1)/(m_2)`

3) Two equations are coincidental if they have the same slope and the same y intercept

`\begin{gathered} \text{That is: m}_1=m_2_{} \\ \text{and c}_1=c_2 \end{gathered}`