Which of the following lines is parallel to the line 3x - 4y + 5 = 0?

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Question: Which of the following lines is parallel to the line 3x - 4y + 5 = 0?

Options:

Correct Answer: 6x - 8y + 10 = 0

Solution:

Parallel lines have the same slope. The slope of the given line is 3/4, and the line 6x - 8y + 10 = 0 also has the same slope.

Which of the following lines is parallel to the line 3x - 4y + 5 = 0?

Which of the following lines is parallel to the line 3x - 4y + 5 = 0?

Step 1: Identify the equation of the given line, which is 3x - 4y + 5 = 0.
Step 2: Rearrange the equation into slope-intercept form (y = mx + b) to find the slope.
Step 3: To rearrange, isolate y: Start with 3x - 4y + 5 = 0.
Step 4: Move 3x and 5 to the other side: -4y = -3x - 5.
Step 5: Divide everything by -4 to solve for y: y = (3/4)x + 5/4.
Step 6: Identify the slope (m) from the equation, which is 3/4.
Step 7: To find a parallel line, we need another line with the same slope of 3/4.
Step 8: Check the other line options given (like 6x - 8y + 10 = 0) to see if they have the same slope.
Step 9: Rearrange the second line (6x - 8y + 10 = 0) into slope-intercept form to find its slope.
Step 10: Isolate y: -8y = -6x - 10.
Step 11: Divide everything by -8: y = (3/4)x + 5/4.
Step 12: Confirm that the slope of the second line is also 3/4, which means it is parallel.

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