Line a is represented by the equation y=14x+8 . How do these equations compare to line a? Drag and drop the equations into the boxes to complete the table. Parallel to line a Perpendicular to line a Neither parallel nor perpendicular to line a y=14x+1y=4x−8y=−4x−3

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.

Adetunmbiadekunle Adetunmbiadekunle · Answer 2 · 2021-10-19T11:25:05+02:00

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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