Line a is represented by the equation y=−2x+3 . 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=2x−1y=−2x+5y=12x+7

Line a is written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept. The slope of line a, the number in place of m, is -2.

Any line parallel to line a will have the same slope as line a, -2. The only line with this slope is y=-2x+5.

Any line perpendicular to this line will have a slope that is the negative reciprocal (this means the opposite sign and flipped upside down). This means that the slope of any line that is perpendicular to line a will have a slope of 1/2. The only line that has a slope of 1/2 is y=1/2x+7.

abidemiokin abidemiokin · Answer 2 · 2021-11-03T11:34:35+01:00

For two lines to be parallel, they must have the same slope. This shows that the equation is parallel to y = -2x + 5 since they have the same slope

For two lines to be perpendicular, the product of their slope must be -1. Hence the line y=−2x+3 is perpendicular to the line y = 1/2 x + 7 since the product of -2 and 1/2 is -1

The standard form of finding the equation of a line is expressed as;

y = mx + b

m is the slope of the line

b is the y - intercept

Given the equation y = -2x + 3

Get the slope

mx = -2x

m = -2

The slope of the line is -2.

For two lines to be parallel, they must have the same slope. This shows that the equation is parallel to y = -2x + 5 since they have the same slope

For two lines to be perpendicular, the product of their slope must be -1. Hence the line y=−2x+3 is perpendicular to the line y = 1/2 x + 7 since the product of -2 and 1/2 is -1

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