Question

The lines described by `y=(a+12)x+3` and `y=4ax` are parallel. What is the value of `a`?

Answer 1

`a=4`

Explanation:

`• " parallel lines have equal slopes"`

`"both equations are in "color(blue)"slope-intercept form"`

`•color(white)(x)y=mx+b`

`"where m represents the slope and b the y-intercept"`

`•color(white)(x)y=(a+12)x+3rArrm=a+12`

`•color(white)(x)y=4axrArrm=4a`

`rArr4a=a+12larrcolor(red)" equal slopes"`

`"subtract a from both sides"`

`rArr3a=12`

`"divide both sides by 3"`

`rArra=4`