Question

Determine the equation of the line that is parallel to the given line, through the given point.

3x+2y = 10; (8,-11)

Answer 1

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

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)

`3x+2y = 10`

First, we must organize this given equation in slope-intercept form. This will help us identify its slope.

`3x+2y = 10`

Subtract 3x from both sides

`2y = -3x+10`

Divide both sides by 2

`y = -(3)/(2) x+5`

Now, we can identify clearly that
`-(3)/(2)` is in the place of m in
`y=mx+b`, making it the slope. Because parallel lines have the same slope, this makes the slope of the line we're currently solving for
`-(3)/(2)` as well. Plug this number into
`y=mx+b`:

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

2) Determine the y-intercept (b)

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

Plug in the given point (8,-11) and solve for b

`-11=-(3)/(2)(8)+b\\-11=-(24)/(2)+b\\-11=-12+b`

Add 12 to both sides

`1=b`

Therefore, the y-intercept of the line is 1. Plug this back into
`y=-(3)/(2)x+b`:

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

I hope this helps!