If two linear equations are represented by the lines y = 2x + 1 and y = 2x - 3, what can be inferred about their relationship?
Practice Questions
1 question
Q1
If two linear equations are represented by the lines y = 2x + 1 and y = 2x - 3, what can be inferred about their relationship?
They intersect at one point.
They are parallel.
They coincide.
They are perpendicular.
Both lines have the same slope (2) but different y-intercepts, indicating they are parallel.
Questions & Step-by-step Solutions
1 item
Q
Q: If two linear equations are represented by the lines y = 2x + 1 and y = 2x - 3, what can be inferred about their relationship?
Solution: Both lines have the same slope (2) but different y-intercepts, indicating they are parallel.
Steps: 5
Step 1: Identify the equations of the lines. The first line is y = 2x + 1 and the second line is y = 2x - 3.
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 of both lines. The y-intercept is the number added at the end of the equation. For the first line, the y-intercept is 1, and for the second line, it is -3.
Step 4: Compare the slopes and y-intercepts. Since both lines have the same slope (2) but different y-intercepts (1 and -3), they will never intersect.
Step 5: Conclude that the lines are parallel because they have the same slope and different y-intercepts.
