What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?

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Question: What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?

Options:

Correct Answer: -1/2

Solution:

The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.

What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?

What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?

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

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