Question

The equation of line L, is y = 5x + 1

The equation of line L, is 2y - 10x + 3 = 0
Show that these two lines are parallel.

Answer 1

They are parallel because they both have the same gradient of 5.

Explanation:

For lines to be parallel they need to contain the same gradient.

1. therefore we rearrange the second equation to get y the subject so it's in the format of y=mx+c

2. 2y-10x+3=0

- we +10x and -3 on both sides to get y on its own

2y=10x-3

- we divide each side by 2 as we want y not 2y

y=5x-
`(3)/(2)`

3. From this we can see that both the equation contains the same gradient (5)

therefore, they are parallel.