Question

What Is `y+3=7(x-2)` written in standard forma?

Answer 1

`7x-y = 17`

Explanation:

Standard form: `ax+by=c`
Note that `a`, `b`, and `c` are integers and `a` is positive.

`y+3=7(x)+7(-2) " "" "" "" "` (distributive property)

`y+3=7x-14 " "" "" "" "" "" "color(white)"-."` (simplify)

`y=7x-14-3 " "" "" "" "" "" "color(white)"-."` (isolate the `y`)

`y=7x-17 " "" "" "" "" "" "" "" "` (simplify)

`-7x + y = -17 " "" "" "" "" "" "` (move the `x` term)

`7x - y = 17 " "" "" "" "" "" "" "" "` (multiply by `-1`)

Answer 2

`y=7x-17larr` Slope intercept form

`7x-y=17 larr`Standard form

Explanation:

Consider the `color(blue)(7)color(green)((x-2))`

Multiply everything inside the brackets by 7

`color(green)([color(blue)(7xx) x] +[color(blue)(7xx)(-2)]`

`" "[7x] +" " [-14]`

`" "7x-14`
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Putting it all together

`y+3=7x-14`

Subtract `color(red)(3)` from both sides

`color(green)(y+3color(red)(-3)" "=" "7x-14color(red)(-3)`

`y+0=7x-17`

`y=7x-17larr` Slope intercept form
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`7x-y=17 larr`Standard form