Question

What is an equation of the line that passes through the point (-5,-2)and is parallel to the line x-y=5?

Answer 1

`y=x+3`

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 (m)

1) Determine the slope (m)

`x-y=5`

Rearrange this given equation into slope-intercept form. This will make it easier for us to identify the slope.

Subtract x from both sides of the equation

`x-y-x=-x+5\\-y=-x+5`

Divide both sides by -1 to isolate y

`y=x-5`

Now, we can identify clearly that the slope of this line is 1. Because parallel lines have the same slopes, a line parallel to this one would also have a slope of 1. Plug this into
`y=mx+b`:

`y=1x+b\\y=x+b`

2) Determine the y-intercept (b)

`y=x+b`

Plug in the given point (-5,-2)

`-2=-5+b`

Add 5 to both sides

`-2+5=-5+b+5\\3=b`

Therefore, the y-intercept of the line is 3. Plug this back into
`y=x+b`:

`y=x+3`

I hope this helps!