Question

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

Answer 1

Answer:

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

Step-by-step 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.