How do I describe the characteristics for a line to be parallel to another including something about the y-intercepts?

Question

 the full question on my homework sheet is: Describe the characteristics for a line to be parallel to another including both the slope and y-intercept.

I just don't understand the y-intercept part and how it relates to parallel lines

Answer 1

The characteristics of parallel lines include the following:

 

1) equal slopes

2) unequal y-intercepts

 

Parallel lines must have unequal y-intercepts because otherwise the lines would be identical, in which case they would not be parallel but one and the same.

Answer 2

The y-intercept is where a line crosses the y-axis, which is when x = 0.

 

Parallel lines on a graph mean that two or more lines have the exact same slope as one another (which is what makes them parallel: they cannot touch, and if their slopes differ, they eventually will sooner or later). The y-intercept is a tool to see just how close or how far each line is to one another:

 

y = 3x + 5

y = 3x + 4

y = 3x + 6,783,648,213,464,987,123

 

Each of these lines are parallel: they each have the exact same slope, so no matter what value up put into x, they will never touch one another.

When we put 0 into the value of x, we see where they cross the y-axis--find the y-intercept:

y = 3 * 0 + 5

y = 0 + 5
y = 3 * 0 + 4

y = 0 + 4

y = 3 * 0 + 6,783,648,213,464,987,123

y = 0 + 6,783,648,213,464,987,123

 

The y-intercept, thus, is a tool to help define a point on the line to determine where on the graph it resides.

Answer 3

If two lines are parallel, then they never intersect.

 

The two lines have the same slope, but have different y-intercepts (if the slopes are the same and the y-intercepts are the same, then the lines would be the same line).