What is the slope of the line perpendicular to the line 4x - 5y + 10 = 0? (2022)

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Question: What is the slope of the line perpendicular to the line 4x - 5y + 10 = 0? (2022)

Options:

Correct Answer: -4/5

Exam Year: 2022

Solution:

The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.

What is the slope of the line perpendicular to the line 4x - 5y + 10 = 0? (2022)

What is the slope of the line perpendicular to the line 4x - 5y + 10 = 0? (2022)

Step 1: Start with the equation of the line: 4x - 5y + 10 = 0.
Step 2: Rearrange the equation to the slope-intercept form (y = mx + b), where m is the slope.
Step 3: Move 4x and 10 to the other side: -5y = -4x - 10.
Step 4: Divide every term by -5 to solve for y: y = (4/5)x + 2.
Step 5: Identify the slope (m) of the original line, which is 4/5.
Step 6: To find the slope of the line that is perpendicular, take the negative reciprocal of 4/5.
Step 7: The negative reciprocal of 4/5 is -5/4.

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