Question

In this diagram which equation could you prove to be true in order to conclude that the lines are parallel

Answer 1

`D)(B)/(A) =(C)/(D)`

Explanation:

Remember that parallel lines have the same slope, and the formula for slope is:

`m=(y2-y1)/(x2-x1)`

So now, if you insert the values of each line, you would get:

Point 2 line 1 (0,B)O

Point 1 line 1 (-A,0)

Insert into the formula:

`m=(y2-y1)/(x2-x1)\\m=(B-0)/(0-(-A))\\m=(B)/(A)`

That is the slope of line 1.

Point 2 line 2 (D,0)

Point 1 line 2 (0,-C)

Insert into the formula:

`m=(y2-y1)/(x2-x1)\\m=(0-(-C))/(D-0)\\m=(C)/(D)`

So the slope for the line number 2 is:
`m=(C)/(D)`

If both slopes are equal we can prove that they are parallel, so the correct option would be
`D)(B)/(A) =(C)/(D)`

Answer 2

I would say that the correct answer is D. because y is always the numerator while x is the denominator for the equation y2 - y1/x2 - x1 which means if there is two y's or two x's on the same line you subtract the second one from the first one. If there is only one y and/or x and the other is 0 on the same line, it stays at y or x without subtracting y2 - y1 or x2 - x1.

Since b is on the y coordinate and -a is on the x coordinate, you would make it b/a while -a is gonna be a positive since the lines are going up and to the right. Now, since c is the y coordinate and d is the x coordinate, make C the numerator and d the denominator since y is always the numerator and x is the denominator for these parallel line figures on the graph and the equation will be equaled to the fraction to the other fraction for parallel lines.

So, your answer would be D. b/a = c/d

Hope this helps, and is correct!

~ ShadowXReaper069