We are given first equation: −2x+3y=12.
Converting it in slope-intercept form
3y=2x + 12
y= 2/3 x + 12/3
y= 2/3 x + 4.
Slope of the given equation is 2/3.
Note: When slopes are same, lines would be parallel.
When slope are negative reciprocals, lines would be perpendicular.
When neither same nor negative reciprocal, the lines neither parallel nor perpendicular.
1) First option : -2x+y=12.
In slope-intercept form y = 2x +12.
Slope is 2 there.
Neither parallel nor perpendicular to the line −2x+3y=12.
2) 3x+2y=-2
In slope-intercept form y = -3/2 x - 1.
Slope = -3/2.
Slope are negative reciprocal to slope of −2x+3y=12 equation.
Therefore, lines are perpendicular.
3) y=2/3x-1
Slope = 2/3.
Slopes are same therefore lines are parallel.
4) -2x+3y=11
y = 2/3 x + 11/3.
Slopes are same therefore lines are parallel.