Question

The equation for line r can be written as y=-1/4x+3. Line s which is parallel to lone r includes the point (-4,3). What is the equation of line s?

Answer 1

`y=-(1)/(4)x+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 the same slope

1) Determine the slope of line S using line R (m)

`y=-(1)/(4) x+3`

We can identify clearly that the slope of the line is
`-(1)/(4)`, as it is in the place of m. Because parallel lines always have the same slope, the slope of line S would also be
`-(1)/(4)`. Plug this into
`y=mx+b`:

`y=-(1)/(4)x+b`

2) Determine the y-intercept of line S (b)

`y=-(1)/(4)x+b`

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

`3=-(1)/(4)(-4)+b\\3=1+b`

Subtract 1 from both sides to isolate b

`3-1=1+b-1\\2=b`

Therefore, the y-intercept is 2. Plug this back into
`y=-(1)/(4)x+b`:

`y=-(1)/(4)x+2`

I hope this helps!