Question

What is an equation of the line that passes through the point (-6,-8) and is parallel to the line x-2y=6?

Answer 1

`y=(1)/(2)x-5`

Explanation:

Hi there!

What we need to know:

• Linear equations are typically organized in slope-intercept form:
  `y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
• Parallel lines always have the same slope and different y-intercepts

1) Determine the slope (m)

`x-2y=6`

Rearrange this equation into slope-intercept form (this will help us find the slope)

Subtract x from both sides

`x-2y-x=6-x\\-2y=-x+6`

Divide both sides by -2

`y=(1)/(2) x-3`

Now, we can identify clearly that the slope of the given line is
`(1)/(2)` since it's in the place of m. Because parallel lines always have the same slopes, the line we're currently solving for would therefore have a slope of
`(1)/(2)` as well. Plug this into
`y=mx+b`:

`y=(1)/(2)x+b`

2) Determine the y-intercept (b)

`y=(1)/(2)x+b`

Plug in the given point (-6,-8)

`-8=(1)/(2)(-6)+b\\-8=-3+b`

Add 3 to both sides to isolate b

`-8+3=-3+b+3\\-5=b`

Therefore, the y-intercept is -5. Plug this back into
`y=(1)/(2)x+b`:

`y=(1)/(2)x-5`

I hope this helps!