Question

Determine whether the lines are perpendicular, parallel, or neither. Y=3x-5 and 12x+4y=8

Answer 1

The two lines are neither perpendicular nor parallel to each other.

Explanation:

Comparing the slopes of two lines is a great way for telling whether they are perpendicular or parallel to each other.

To find the slope of the lines, start by rewriting their equations in the slope-intercept form:

`y = mx + b`,

where

• 
  `m` is the slope of the line, and
• 
  `b` is the y-intercept (the y-value of the point where the line crosses the y-axis.)

The first line is already in this form. Its slope (the number in front of
`x`) is equal to
`3`.

Subtract
`12x` from both sides of the equation of the second line:

`4y = -12x + 8`.

Divide both sides by four:

`y = -3x + 2`.

The slope of this line will be equal to
`(-3)`.

Two lines are parallel if their slopes are the same. They are perpendicular to each other if the product of their slope is equal to
`(-1)` (i.e. the two slopes are inverse reciprocal of one another.) Neither is the case for these two lines. In conclusion, these two lines are neither parallel nor perpendicular to each other.