Question

Don’t quite understand.

Answer 1

(a) Same slope and different y intercept

Explanation:

Given

`y = (3)/(7)x + 11`

`-3x + 7y = 13`

Required

Are the lines, parallel?

To do this, we first convert both equations to slope intercept;

`y = mx+ b`

Where

`m = slope`

So, we have:

`y = (3)/(7)x + 11`

`-3x + 7y = 13`

Solve for 7y

`7y = 3x + 13`

Solve for y

`(7y)/(7) = (3x)/(7) + (13)/(7)`

`y = (3)/(7)x + (13)/(7)`

So, the two equations are now:

`y = (3)/(7)x + 11`

`y = (3)/(7)x + (13)/(7)`

When two lines have the same slope but different y intercepts, then they are parallel.

Recall that:

In
`y = mx + b`

`m = slope`

`b = y \ intercept`

So:

In
`y = (3)/(7)x + 11` and
`y = (3)/(7)x + (13)/(7)`

The slopes are:

`m = (3)/(7)` and
`m = (3)/(7)`

The y intercepts are:

`b = 11` and
`b = (13)/(7)`

Since the values of m (the slope) are the same and the values of b (the y intercepts) are differenr, then they are parallel