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Answer:
y = 4
Step-by-step explanation:
Given the equation of the line, y = 6, passing through point (3, 4):
By definition, parallel lines have the <u>same slope</u>.
The linear equation, y = 6 is a horizontal line with a zero slope. Therefore, the parallel line must also have the same slope = 0.
Plug the given values from the point (3, 4) into the slope-intercept form:
y = mx + b
where: y = 4, m = 0, and x = 3. We need to solve for the y-intercept, b:
y = mx + b
4 = 0(3) + b
4 = 0 + b
4 = b
Therefore, the y-intercept is (0, 4).
For horizontal lines, the y-coordinate = 4 stays the same, while having different x-coordinates.
Therefore, the equation that is parallel to y = 6 is y = 4.
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