Which of the following lines is parallel to the line 4x - 5y + 10 = 0?

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Question: Which of the following lines is parallel to the line 4x - 5y + 10 = 0?

Options:

Correct Answer: y = (4/5)x - 3

Solution:

The slope of the given line is 4/5. A line parallel to it must have the same slope, hence y = (4/5)x - 3.

Which of the following lines is parallel to the line 4x - 5y + 10 = 0?

Which of the following lines is parallel to the line 4x - 5y + 10 = 0?

Step 1: Start with the given line equation: 4x - 5y + 10 = 0.
Step 2: Rearrange the equation to the slope-intercept form (y = mx + b).
Step 3: Move 4x and 10 to the other side: -5y = -4x - 10.
Step 4: Divide everything by -5 to solve for y: y = (4/5)x + 2.
Step 5: Identify the slope (m) of the line, which is 4/5.
Step 6: Remember that parallel lines have the same slope.
Step 7: Write the equation of a new line with the same slope (4/5) but a different y-intercept, for example: y = (4/5)x - 3.

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