Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.
y = 3x + 3
-7x - 2y = -19
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
The first equation is in slope-intercept form, y = mx + b, where m is the slope. In this case, the slope is 3.
The second equation can be rewritten in slope-intercept form by solving for y:
-7x - 2y = -19
-2y = 7x - 19
y = (7/2)x - 19/2
So the slope of the second equation is 7/2.
Since the slopes of these two lines are not equal, they are not parallel.
To determine if they are perpendicular, we can calculate the product of their slopes:
3 * (7/2) = 21/2 ≠ -1
Since the product of their slopes is not -1, the lines are not perpendicular either.
Therefore, the lines represented by the pair of equations y = 3x + 3 and -7x - 2y = -19 are neither parallel nor perpendicular.