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

Jul 16, 2017

$7 x - y = 17$

#### Explanation:

Standard form: $a x + b y = c$
Note that $a$, $b$, and $c$ are integers and $a$ is positive.

$y + 3 = 7 \left(x\right) + 7 \left(- 2\right) \text{ "" "" "" }$ (distributive property)

$y + 3 = 7 x - 14 \text{ "" "" "" "" "" "color(white)"-.}$ (simplify)

$y = 7 x - 14 - 3 \text{ "" "" "" "" "" "color(white)"-.}$ (isolate the $y$)

$y = 7 x - 17 \text{ "" "" "" "" "" "" "" }$ (simplify)

$- 7 x + y = - 17 \text{ "" "" "" "" "" }$ (move the $x$ term)

$7 x - y = 17 \text{ "" "" "" "" "" "" "" }$ (multiply by $- 1$)

Jul 17, 2017

$y = 7 x - 17 \leftarrow$ Slope intercept form

$7 x - y = 17 \leftarrow$Standard form

#### Explanation:

Consider the $\textcolor{b l u e}{7} \textcolor{g r e e n}{\left(x - 2\right)}$

Multiply everything inside the brackets by 7

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

$\text{ "[7x] +" } \left[- 14\right]$

$\text{ } 7 x - 14$
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Putting it all together

$y + 3 = 7 x - 14$

Subtract $\textcolor{red}{3}$ from both sides

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

$y + 0 = 7 x - 17$

$y = 7 x - 17 \leftarrow$ Slope intercept form
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$7 x - y = 17 \leftarrow$Standard form