Determine if these problems x+2y=5 and -2x+y=5 are parallel, perpendicular, or neither? Thank you

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mlsiasebs | College Teacher | (Level 1) Associate Educator

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To determine if two lines are parallel, perpendicular or neither we need to compare the value of their slopes.  This requires that we put the equations in the general format of a line y = mx + b.

We can rearrange the first equation

x + 2y = 5

by subtracting x from both sides and then dividing by two to get

y = -(1/2) x + 5/2

so the slope of the line is -1/2 and the y-intercept is 5/2.

For the second equation, we rearrange

-2x + y = 5

by adding 2x to both sides of the equation resulting in

y = 2x + 5

This line has a slope of 2 and a y-intercept of 5.

Perpendicular lines have slopes that are the negative reciprocal of each other.  The negative reciprocal of 2 is -1/2, so these lines are perpendicular.