Question

What lines are parallel to 8x+2y=7. Select all that apply

Answer 1

Step-by-step explanation:

16x+ 4y= 14 is parallel to 8x+2y=7

Answer 2

Step-by-step explanation:

Given:

$8x + 2y = 7$

To find: Lines parallel to given line.

Solution:

Tip: Two lines $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ are parallel if ratio of coefficients of x and y are equal.

i.e.

$\bf \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

Step 1: Write the coefficients of given line

$8x + 2y = 7$

$a_1=8$

$b_1=2$

Step 2: Multiply a constant with both coefficients.

Thus,

$a_2=16$

$b_2=4$

and

$a_3=24$

$b_3=6$

and

$a_4=32$

$b_4=8$

and many more

Note*: One can draw infinite parallel lines in accordance with a given parallel line.

Step 3: Write equations of parallel lines

$16x + 4y = 5$

$24x + 6y = 3$

$32x + 8y = 9$

and many more...

Final answer:

Some lines which are parallel to

$8x + 2y = 7$

are

$\bf \orange{16x + 4y = 5}$

$\bf \green{24x + 6y = 3}$

$\bf \purple{32x + 8y = 9}$

Hope it helps you.

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