What is the slope of the line perpendicular to the line 4x + 3y = 12?

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Question: What is the slope of the line perpendicular to the line 4x + 3y = 12?

Options:

Correct Answer: -4/3

Solution:

The slope of the line 4x + 3y = 12 is -4/3. The slope of the perpendicular line is the negative reciprocal, which is 3/4.

What is the slope of the line perpendicular to the line 4x + 3y = 12?

What is the slope of the line perpendicular to the line 4x + 3y = 12?

Step 1: Start with the equation of the line: 4x + 3y = 12.
Step 2: Rearrange the equation to find the slope. We want to write it in the form y = mx + b, where m is the slope.
Step 3: Subtract 4x from both sides: 3y = -4x + 12.
Step 4: Divide every term by 3 to isolate y: y = -4/3 x + 4.
Step 5: Identify the slope of the original line, which is -4/3.
Step 6: To find the slope of the line that is perpendicular, take the negative reciprocal of -4/3.
Step 7: The negative reciprocal of -4/3 is 3/4.

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