Question

WRITE an equation of the line that passes through the given point and is PARALLEL to the given line.

(10, -12), 3x + 4y = 1

Answer 1

`y=-(3)/(4)x-(9)/(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 (m)

`3x + 4y = 1`

Rearrange the given equation into slope-intercept form (this will help us determine m)

Subtract 3x from both sides to isolate 4y

`3x + 4y-3x = -3x+1\\4y= -3x+1`

Divide both sides by 4 to isolate y

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

Now, we can identify that
`-(3)/(4)` is the slope of the line. Parallel lines have the same slope, so this would also be the slope of the line we're solving for. Plug this into
`y=mx+b`:

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

2) Determine the y-intercept (b)

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

Plug in the given point (10,-12) and solve for b

`-12=-(3)/(4)(10)+b\\-12=-(3)/(2)(5)+b\\-12=-(15)/(2)+b`

Add
`(15)/(2)` to both sides to isolate b

`-12+(15)/(2)=-(15)/(2)+b+(15)/(2)\\-12+(15)/(2)=b\\-(9)/(2) =b`

Therefore, the y-intercept is
`-(9)/(2)`. Plug this back into
`y=-(3)/(4)x+b`:

`y=-(3)/(4)x-(9)/(2)`

I hope this helps!