Question

Is y=3x+4 parallel or perpendicular

Answer 1

Answer: $y=3x+4$ is parallel to $y=3x+7$

Step-by-step explanation:

The complete exercise is: "Is $y=3x+4$ parallel, perpendicular or neither to $y=3x+7$?"

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

First, in order to solve this exercise it is important to remember that, by definition:

1. The slopes of parallel lines are equal.

2. The slopes of perpendicular lines are negative reciprocal.

In this case, you have the following line given in the exercise:

 $y=3x+4$

You can identify that "m" and "b" are:

$m=3\\b=4$

And the other line provided in the exercise is this one:

$y=3x+7$

So, you can identify that:

$m=3\\b=7$

As you can notice, the slopes of both lines are equal; therefore, you can conclude that those lines are parallel.