# How do you solve the equation for y, given y+7x=9 then find the value for each value of x: -1, 0, 4?

Nov 1, 2016

$\left(- 1 , 16\right) \text{ "(0.9)" } \left(4 , - 19\right)$

#### Explanation:

$y + 7 x = 9$

There are 2 variables in this equation, which means that you can't solve it and find ONE unique solution. There are infinitely many solutions.

"Solve for y" means write the equation as $y = \ldots \ldots \ldots .$

$y + 7 x - 7 x = 9 - 7 x \text{ } \leftarrow$ subtract $7 x$ from each side

$\text{ "y = -7x+9" } \leftarrow$ equation of a straight line

Now you have been given various values of $x$. Use each in turn in the equation and find the corresponding values of $y$

$\text{ } y = - 7 \textcolor{m a \ge n t a}{x} + 9$

$\textcolor{m a \ge n t a}{x = - 1} \rightarrow \text{ } y = - 7 \textcolor{m a \ge n t a}{\left(- 1\right)} + 9$
$\textcolor{w h i t e}{\times \times \times . \times \times x} y = + 7 + 9 = 16$

$\textcolor{m a \ge n t a}{x = 0} \rightarrow \text{ } y = - 7 \textcolor{m a \ge n t a}{\left(0\right)} + 9$
$\textcolor{w h i t e}{\times \times \times . . \times \times} y = 0 + 9 = 9$

$\textcolor{m a \ge n t a}{x = 4} \rightarrow \text{ } y = - 7 \textcolor{m a \ge n t a}{\left(4\right)} + 9$
$\textcolor{w h i t e}{\times \times \times \ldots \times \times} y = - 28 + 9 = - 19$

What you have actually found is three points, $\left(x , y\right)$ on a line.
$\left(- 1 , 16\right) \text{ "(0.9)" } \left(4 , - 19\right)$