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Answer:
y=2x−1 is neither parallel nor perpendicular to line a; y=−2x+5 is parallel to line a; y=1/2x+7 is perpendicular to line a.
Step-by-step explanation:
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.
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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