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Prove that 3x + y = 7 + y and 3(x + y) = 2 + 3x are perpendicular

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Answer:

Since one line is vertical, and one line is horizontal, the lines are perpendicular.

Explanation:

The product of the slopes of perpendicular lines is -1.

We find the slopes of the 2 lines and multiply them together.

If the product equals -1, then the lines are perpendicular.

To find the slopes of the lines, we write each equation in the y = mx + b form, where m is the slope. In other words, we solve each equation for y.

3x + y = 7 + y

Subtract y from both sides.

3x = 7

x = 7/3

This is not the y = mx + b form since there is no y in the equation. A line with equation x = k, where k is a number, is a vertical line that passes through the point (k, 0), and the x-coordinate of all points on the line is k.

3(x + y) = 2 + 3x

3x + 3y = 2 + 3x

Subtract 3x from both sides.

3y = 2

y = 2/3

y = 0x + 2/3

Slope = m = 0

A line with 0 slope is a horizontal line.

Since one line is vertical, and one line is horizontal, the lines are perpendicular.

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