If two linear equations have the same slope but different y-intercepts, what can

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Question: If two linear equations have the same slope but different y-intercepts, what can be inferred about their graphs?

Options:

Correct Answer: They are parallel lines.

Solution:

Lines with the same slope but different y-intercepts are parallel and will never intersect.

If two linear equations have the same slope but different y-intercepts, what can be inferred about their graphs?

If two linear equations have the same slope but different y-intercepts, what can be inferred about their graphs?

Step 1: Understand what a linear equation looks like. A linear equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
Step 2: Identify what slope means. The slope (m) tells us how steep the line is and the direction it goes. If two lines have the same slope, they rise or fall at the same rate.
Step 3: Understand what y-intercept means. The y-intercept (b) is the point where the line crosses the y-axis. Different y-intercepts mean the lines start at different points on the y-axis.
Step 4: Combine the information. If two lines have the same slope but different y-intercepts, they will never meet because they are always the same distance apart.
Step 5: Conclude that these lines are parallel. Parallel lines run alongside each other and will never intersect.

Linear Equations – Linear equations can be represented in the form y = mx + b, where m is the slope and b is the y-intercept.
Slope and Y-Intercept – The slope indicates the steepness of the line, while the y-intercept indicates where the line crosses the y-axis.
Parallel Lines – Lines that have the same slope but different y-intercepts are parallel and do not intersect.