Question

What is the first step when constructing a line parallel to the x-axis of a coordinate plane through a point?

Answer 1

Two lines in a plane that never intersect are called parallel lines. Working with parallel lines in the coordinate plane is fairly straightforward. The reason for this is because the slope of a line is essentially the measure of an angle of a line from a perfectly horizontal line (or the x-axis). Thus, in the coordinate plane, if we want two different lines to never intersect, we simply apply the same slopes to them.

Answer 2

Would you like an example?

Answer 3

yes please.

Answer 4

Okay. :)

Answer 5

Let's take a look at the following equations:
y = 2x - 1
4x = 6x - y + 2
How do we determine if these lines are parallel or if they intersect at some point?
First, it will help to put both equations in slope-intercept form. The first equation is already of this form so we do not need to change it. The second equation, however, needs to be manipulated. Let’s work it out:
4x = 6x - y + 2
Now, we add y to both sides of the equation to get
4x + y = 6x + 2
Subtracting 4x from both sides of the equation gives us
y = 2x + 2
Now, if we look at both equations, we notice that they both have slopes of 2. Since both lines “rise” two units for every one unit they “run,” they will never intersect. Thus, they are parallel lines.