Tell whether the lines for the pair of equations are parallel, perpendicular, or neither. y= -2/3x + 1 2x -3y = -3
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the lines.
The given equations are:
1) y = -2/3x + 1
2) 2x - 3y = -3
To compare the slopes, we need to rewrite equation 2 in slope-intercept form (y = mx + b), where "m" represents the slope. Let's convert equation 2 into slope-intercept form:
2x - 3y = -3
Rearranging the equation:
-3y = -2x - 3
Dividing every term by -3:
y = 2/3x + 1
Comparing the slopes of the two equations:
Slope of equation 1: -2/3
Slope of equation 2: 2/3
Since the slopes are negative reciprocals of each other (i.e., multiplying the slopes together will equal -1), the lines are perpendicular.