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.
<u>Note:</u><em> When slopes are same, lines would be parallel.</em>
<em>When slope are negative reciprocals, lines would be perpendicular.</em>
<em>When neither same nor negative reciprocal, the lines neither parallel nor perpendicular.</em>
1) First option : -2x+y=12.
In slope-intercept form y = 2x +12.
Slope is 2 there.
<h3>Neither parallel nor perpendicular to the line −2x+3y=12.</h3>
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.
<h3>Therefore, lines are perpendicular.</h3>
3) y=2/3x-1
Slope = 2/3.
<h3>Slopes are same therefore lines are parallel.</h3>
4) -2x+3y=11
y = 2/3 x + 11/3.
<h3>Slopes are same therefore lines are parallel.</h3>
