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REY [17]
4 years ago
15

Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −2x+3y=12?

Mathematics
1 answer:
givi [52]4 years ago
4 0

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.

<em>Slope of the given equation is 2/3.</em>


<em>Note: 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>
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