Question

Why or why not do you think use the y intercept when trying to determine if two lines are parallel or perpendicular ?

Answer 1

See answer below

Explanation:

Given: Why or why not do we not use the `y`-intercept to decide if two lines are parallel or perpendicular?

The equation of a line in slope-intercept form is `y = mx + b`

where `m =` slope, and the `y-`intercept `= (0, b)`

Ex. of two parallel lines: `y_1 = 3x +2; " "y_2 = 3x -5`

When two lines are parallel, they have the same slope, but the `y-`intercept is not the same.

Ex. of two perpendicular lines: `y_3 = 3/4x + 2; " " y_4 = -4/3x + 2`

Ex. of two perpendicular lines: `y_5 = 2/7x -1; " " y_6 = -7/2x + 3`

When two lines are perpendicular, the slopes are negative reciprocals (`m_2 = -1/m_1; " "m_1 xx m_2 = -1`).

From the examples above you can see that the `y-`intercepts can be equal, but they don't have to be.