Question

the line -6x-2y = 21 is parallel to the line 2x-3y+7 =0, yes or no

Answer 1

no

the answer of this question is no

Answer 2

SOLUTION

TO DETERMINE

Yes / No the below statement :

The line - 6x - 2y = 21 is parallel to the line 2x - 3y + 7 = 0

EVALUATION

Here the given equation of the lines are

- 6x - 2y = 21 and 2x - 3y + 7 = 0

Equation of the 1st line is

- 6x - 2y = 21

Which can be rewritten as

2y = - 6x - 21

$\displaystyle\sf{ \implies \: y = - 3x - \frac{21}{2} }$

Which is of the form y = mx + c

So slope of first line = - 3

The equation of the 2nd line is

2x - 3y + 7 = 0

Which can be rewritten as

3y = 2x + 7

$\displaystyle\sf{ \implies \: y = \frac{2}{3} x + \frac{7}{3} }$

Which is of the form y = mx + c

So slope of 2nd line $\displaystyle\sf{ = \frac{2}{3} }$

Since slope of the given two lines are unequal

So the given two lines are not parallel

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