Question

Find the equation of the line that passes through (−3, −4) that is parallel to the line 2x-y = 5

Answer 1

`y=2x+2`

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 x is 0)
• Parallel lines always have equal slopes

1) Determine the slope (m)

`2x-y = 5`

To do so, we must organize the given equation into slope-intercept form to identify the value in place of m.

Subtract 2x from both sides (isolate y)

`2x-y -2x= -2x +5\\-y= -2x +5`

Divide both sides by -1 (isolate y)

`y= 2x -5`

Now, from this equation, we can tell that the number in the place of m in
`y=mx+b` is 2. Because parallel lines have equal slopes, the slope of the line we're currently solving for would also be 2. Plug this slope into
`y=mx+b`:

`y=2x+b`

2) Determine the y-intercept (b)

`y=2x+b`

Plug in the given point (-3,-4) and solve for b

`-4=2(-3)+b\\-4=-6+b`

Add 6 to both sides to isolate b

`-4+6=-6+b+6\\2=b`

Therefore, the y-intercept is 2. Plug this back into
`y=2x+b`:

`y=2x+2`

I hope this helps!