Are the lines y=4 and 4y=6 parallel, perpendicular, or neither?
Understand the Problem
The question is asking us to determine the relationship between the two lines given by the equations y=4 and 4y=6. To solve this, we need to convert both equations into slope-intercept form (y=mx+b) to compare their slopes. This will help us identify if the lines are parallel, perpendicular, or neither.
Answer
The two lines are parallel.
Answer for screen readers
The two lines given by the equations $y = 4$ and $4y = 6$ are parallel.
Steps to Solve
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Rewrite the first equation
The first equation is already in slope-intercept form. It is given by:
$$ y = 4 $$
This indicates a horizontal line where the slope (m) is 0. -
Rewrite the second equation
We need to rearrange the second equation into slope-intercept form. The equation is:
$$ 4y = 6 $$
To get y by itself, divide both sides by 4:
$$ y = \frac{6}{4} $$
This simplifies to:
$$ y = \frac{3}{2} $$
This also indicates another horizontal line with a slope of 0. -
Identify the relationship between the two lines
Now we have both lines: -
Line 1: $y = 4$ (slope = 0)
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Line 2: $y = \frac{3}{2}$ (slope = 0)
Both lines have the same slope, meaning they are parallel lines.
The two lines given by the equations $y = 4$ and $4y = 6$ are parallel.
More Information
Parallel lines have the same slope but different y-intercepts. In this case, even though both lines are horizontal, they occupy different positions on the y-axis.
Tips
One common mistake is to assume that if two lines are horizontal, they must intersect. Remember that horizontal lines with different y-values represent parallel lines.
