Question

HELP!!!!!

The equations of four lines are given. Identify which lines are parallel.
Line 1: y=1/3(x+6)
Line 2: y−6=3x
Line 3: y=−3(x−4)
Line 4: 3y+18=x

Answer 1

Line 1 and line 4 are parallel

Step-by-step explanation:

Two lines are said to be parallel if they have same slope.

In order to compare the lines given, we have to write them all in the same form, and then compare their slopes.

Line 1:

$y=\frac{1}{3}(x+6)$

Applying distributive property,

$y=\frac{1}{3}x+2$

Line 2:

$y-6 = 3x\\\rightarrow y=3x+6$

Line 3:

$y=-3(x-4)$

Applying  distributive property,

$y=-3x+12$

Line 4:

$3y+18=x$

re-arranging,

$3y=x-18\\y=\frac{1}{3}x-6$

Now we have rewritten all the lines in the form $y=mx+q$, where m is the slope. By comparing the values of m, we see:

$m_1 = \frac{1}{3}\\m_2=3\\m_3 = -3\\m_4=\frac{1}{3}$

Therefore, the lines which are parallel are line 1 and line 4.

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