Question

67. The line contains the point (4,0) and is parallel
to the line defined by 3x = 2y.

Answer 1

`y=(3)/(2) x-6`

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 of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

• Parallel lines will always have the same slope but different y-intercepts.

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

`3x = 2y`

Switch the sides

`2y=3x`

Divide both sides by 2 to isolate y

`(2y)/(2) = (3)/(2) x\\y=(3)/(2) x`

Now that this equation is in slope-intercept form, we can easily identify that
`(3)/(2)` is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope
`(3)/(2)` . Plug this into
`y=mx+b`:

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

2) Determine the y-intercept

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

Plug in the given point, (4,0)

`0=(3)/(2) (4)+b\\0=6+b`

Subtract both sides by 6

`0-6=6+b-6\\-6=b`

Therefore, -6 is the y-intercept of the line. Plug this into
`y=(3)/(2) x+b` as b:

`y=(3)/(2) x-6`

I hope this helps!