Determine whether each pair of equations are parallel, perpendicular or neither. y+2x=23 y=-2x+11

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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One way to identify the relative position of 2 lines is to compare their slopes.

For instance, if 2 lines are parallel, their slopes must be equal. Or, if 2 lines are perpendicular, the product of their slopes is -1.

The slope could be identified, writing the equation in the standard form:

y = mx + n, where m is the slope and n is the y intercept.

We'll put each given equation in the standard form. We'll start with the first one.

We'll isolate y to the left side:

y = -2x + 23

m1 = -2

The 2nd equation is written in the standard form, already:

y=-2x+11

m2 = -2

Since the slopes m1 = m2 = -2, the lines are parallel.

neela | High School Teacher | (Level 3) Valedictorian

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We recast both equations in the slope intercept form of y = mx+c and then see whether both lines represented by the equations have the same slope m to be parallel.

The first given equation y + 2x = 23 . We  reacast it  as : y = -2x +23....(1)

The other equation y = -2x+11...(1) is in the slope intercept form itself.

Both equations of lines have the same slope of -2. So they are inclined at the same angle to the x axis. So both of the equations represent parallel lines.