Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.%0D%0A%0D%0Ay = x + 1%0D%0A2x – 3y = –3%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Aparallel%0D%0Aparallel%0D%0A%0D%0Aperpendicular%0D%0Aperpendicular%0D%0A%0D%0Aneither
To determine whether the lines for the pair of equations are parallel, perpendicular, or neither, we need to compare their slopes.
The equation of the first line, y = x + 1, is in the form y = mx + b, where m represents the slope. In this case, the slope is 1.
The equation of the second line, 2x - 3y = -3, can be rearranged to slope-intercept form to determine its slope. Subtracting 2x from both sides gives -3y = -2x - 3, and dividing both sides by -3 gives y = (2/3)x + 1. So the slope of the second line is (2/3).
Since the slopes of the lines are different (1 and 2/3), the lines are neither parallel nor perpendicular to each other.