If two linear equations are represented by the lines y = 2x + 3 and y = 2x - 1,

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Question: If two linear equations are represented by the lines y = 2x + 3 and y = 2x - 1, what can be inferred about their relationship?

Options:

Correct Answer: They are parallel lines.

Solution:

Both lines have the same slope (2) but different y-intercepts, indicating they are parallel.

If two linear equations are represented by the lines y = 2x + 3 and y = 2x - 1, what can be inferred about their relationship?

If two linear equations are represented by the lines y = 2x + 3 and y = 2x - 1, what can be inferred about their relationship?

Step 1: Identify the equations of the lines. The first line is y = 2x + 3 and the second line is y = 2x - 1.
Step 2: Look at the slope of both lines. The slope is the number in front of x. For both lines, the slope is 2.
Step 3: Check the y-intercepts. The y-intercept is the number added to the 2x. For the first line, it is +3, and for the second line, it is -1.
Step 4: Since both lines have the same slope (2) but different y-intercepts (3 and -1), they will never intersect.
Step 5: Conclude that the lines are parallel because parallel lines have the same slope but different y-intercepts.

Linear Equations – Understanding the properties of linear equations, including slope and y-intercept.
Parallel Lines – Recognizing that lines with the same slope but different y-intercepts are parallel.