What is the slope of the line perpendicular to the line 5x + 2y = 10?

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Question: What is the slope of the line perpendicular to the line 5x + 2y = 10?

Options:

Correct Answer: -2/5

Solution:

The slope of the line is -5/2. The slope of the perpendicular line is the negative reciprocal, which is 2/5.

What is the slope of the line perpendicular to the line 5x + 2y = 10?

What is the slope of the line perpendicular to the line 5x + 2y = 10?

Step 1: Start with the equation of the line: 5x + 2y = 10.
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 5x from both sides: 2y = -5x + 10.
Step 4: Divide every term by 2 to solve for y: y = -5/2 * x + 5.
Step 5: Identify the slope of the original line, which is -5/2.
Step 6: To find the slope of the line that is perpendicular, take the negative reciprocal of -5/2.
Step 7: The negative reciprocal of -5/2 is 2/5.

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