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Answer:
y=1/4x+1 is parallel to line a; y=4x−8 is neither parallel nor perpendicular to line a; y=−4x−3 is perpendicular to line a.
Step-by-step explanation:
Two lines that are parallel have the same slope.
Line a is written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept. In line a, the value of m is 1/4; this means the slope is 1/4.
The slope of the first line, y=1/4x+1, is 1/4. Since the slopes are the same, the lines are parallel.
None of the other lines have a slope of 1/4, so none of the others are parallel to line a.
Two lines that are perpendicular have slopes that are negative reciprocals; this means their signs are opposite and the fractions representing the slopes are "flipped." Since the slope of line a = 1/4, any line perpendicular to it will have a slope of -4/1, or -4. The only line with a slope of -4 is the last one, y=-4x-3. This is perpendicular to line a.
The remaining line, y=4x-8, is neither perpendicular nor parallel to line a.
The equation y=14x+8 and y = -4x - 3 are neither parallel nor perpendicular
The slope-intercept form of the equation of a line is:
y = mx + c
where m is the slope
c is the y-intercept
Let two equations be represented by y = m₁x + c₁ and y = m₂x + c₂
The two equations are parallel if m₁ = m₂
The two equations are perpendicular if m₁m₂ = -1
For the equation y = 14x + 8
m₁ = 14, c₁ = 8
For the equation y = -4x - 3
m₂ = -4, c₂ = -3
Comparing the two equations above:
m₁ ≠ m₂ (Not parallel)
m₁m₂ = -4(14) = -56 ≠ -1 (Not perpendicular)
Therefore, the equation y=14x+8 and y = -4x - 3 are neither parallel nor perpendicular
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