Answer:
C: The Same Line
Step-by-step explanation:
So to start we need to first know what makes lines parallel or perpendicular. Two parallel lines will have the same slope, but different y-intercepts because we know they never cross. Two perpendicular lines will have opposite-reciprocal slopes, because we know that they intersect at a right angle.
Then, we need to know the slope-intercept form of an equation. The slope intercept form is where
is the slope of the line and
is the y-intercept. We can see that neither equation is in this form, so we have to convert it.
Starting with the first, (I assume despite the typo) we have
So we need to isolate the from everything else.
First, we'll subtract from both sides of the equal sign to get
Second, we'll divide both sides by to get
This means that is the slope and
is the y-intercept of the first line.
Now onto the second we have so we're going to follow the same steps to isolate
.
First, we'll subtract from both sides to get
Second, we'll divide both sides by to get
This means that is the slope and
is the y-intercept of the second line.
Since both of the lines have a slope we know that they are parallel, so we need to check to check if they're the same by looking at the y-intercept. We can see that
is the y-intercept of both lines, so they would be the same line.