Question

Question #dffae

Answer 1

`2y = 3x - 24`

Explanation:

Answers are usually in integer (whole number) form `y = mx + c` where m is the gradient and `c` is the y-intercept. If you multiply both sides by 2, you will get `2y + 12 = 3x - 12` which you rearrange to get the answer above.

Answer 2

It all depends on the structure you wish to end up with.

Explanation:

Assumption: The target format/structure is of form `y=mx+c` where m is the gradient and `c` is a constant.

Given:`" "y+6=3/2(x-4)`

Multiply everything inside the brackets by `3/2` giving

`y+6=3/2 x-12/2`

`y+6=3/2x-6`

Subtract `color(red)(6)` from both sides

`color(green)(y+6color(red)(-6)" "=" "3/2x-6color(red)(-6))`

`y+0" "=" "3/2x-12`

`y=3/2x-12`

Answer 3

`y +6 = 3/2x-6`

`3x -2y -24 =0`

`3x -2y = 24`

There are `3` different forms for the equation of a straight line.

Explanation:

`y +6 = 3/2(x-4)" "larr` remove the bracket by multiplying

`y +6 = 3/2x-6`

This is an equation of a straight line because there is a `x`-term, a `y`-term and a constant term.

It can be given in any one of `3` ways:

`1.` intercept gradient form: `y = mx+c`

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

`y = 3/2x-12`

`2.` General form `ax +by +c =0`

`2y = 3x -24" "larr (xx 2` to get rid of the fraction)

`3x -2y -24 =0`

`3.` Standard form: `ax +by = c`

`3x -2y = 24`