Determine whether the lines are parallel, perpendicular or neither: y+x= -2 and y-x= -2.
My answer is : Perpendicular
Is this correct?
Thanks.
yes
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The given lines have the equations:
1) y + x = -2
2) y - x = -2
We can rewrite equation 1) in slope-intercept form (y = mx + b) by subtracting x from both sides:
y = -x - 2
The slope of equation 1) is -1 because the coefficient of x is -1.
Similarly, equation 2) can be rewritten in slope-intercept form by adding x to both sides:
y = x - 2
The slope of equation 2) is 1 because the coefficient of x is 1.
The slope of one line is the negative reciprocal of the other line's slope, so the lines are perpendicular. In this case, the slope of equation 1) is -1, and the slope of equation 2) is 1, and their product is -1 * 1 = -1.
Therefore, your answer that the lines are perpendicular is correct.