Question

What is the equation of the line that is parallel to Y =-2/3 X +4 and that passes through (-2,-2)?

Answer 1

`y=-(2)/(3)x-(10)/(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 x is 0)
• Parallel lines always have the same slope

1) Determine the slope (m)

`y =-(2)/(3) x +4`

In the given equation,
`-(2)/(3)` is in the place of m, making it the slope. Because parallel lines always have the same slope, the slope of the line we're currently solving for is
`-(2)/(3)`. Plug this into
`y=mx+b`:

`y=-(2)/(3)x+b`

2) Determine the y-intercept (b)

`y=-(2)/(3)x+b`

Plug in the given point (-2,-2) to solve for b

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

Subtract
`(4)/(3)` from both sides to isolate b

`-2-(4)/(3)=(4)/(3)+b-(4)/(3)\\-(10)/(3) =b`

Therefore, the y-intercept of the line is
`-(10)/(3)`. Plug this back into
`y=-(2)/(3)x+b`:

`y=-(2)/(3)x-(10)/(3)`

I hope this helps!