Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.
y=-3/4x+2
3x-4y=-8
y = (-3/4) x + 2
y = (+3/4) x + 2
slopes are -3/4 and +3/4
if they were the same, then parallel
if one were - 1/the other, then perpendicular
so neither
To determine whether the lines for the pair of equations are parallel, perpendicular, or neither, we need to compare the slopes of the lines.
First, let's rearrange the second equation, 3x - 4y = -8, to the slope-intercept form, which is y = mx + b, where m represents the slope:
3x - 4y = -8
-4y = -3x - 8
y = 3/4x + 2
Now we have both equations in slope-intercept form:
y = -3/4x + 2
y = 3/4x + 2
We can see that the slopes of the lines are -3/4 and 3/4.
Since the slopes are negative reciprocals of each other (the product of the slopes is -1), the lines are perpendicular.