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

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

Options:

Correct Answer: 4/3

Solution:

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

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

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

Step 1: Start with the equation of the line: 3x + 4y = 12.
Step 2: Rearrange the equation to the slope-intercept form (y = mx + b) to find the slope. Subtract 3x from both sides: 4y = -3x + 12.
Step 3: Divide every term by 4 to isolate y: y = -3/4 x + 3.
Step 4: Identify the slope (m) of the line from the equation. The slope is -3/4.
Step 5: To find the slope of the line that is perpendicular, take the negative reciprocal of -3/4. The negative reciprocal is 4/3.

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