# How do you graph 9x+2y=5?

Oct 27, 2017

See a solution process below:

#### Explanation:

First, solve for two points which solve the equation and plot these points:

First Point: For $x = 1$

$\left(9 \cdot 1\right) + 2 y = 5$

$9 + 2 y = 5$

$- \textcolor{red}{9} + 9 + 2 y = - \textcolor{red}{9} + 5$

$0 + 2 y = - 4$

$2 y = - 4$

$\frac{2 y}{\textcolor{red}{2}} = - \frac{4}{\textcolor{red}{2}}$

$y = - 2$ or $\left(1 , - 2\right)$

Second Point: For $x = - 1$

$\left(9 \cdot - 1\right) + 2 y = 5$

$- 9 + 2 y = 5$

$\textcolor{red}{9} - 9 + 2 y = \textcolor{red}{9} + 5$

$0 + 2 y = 14$

$2 y = 14$

$\frac{2 y}{\textcolor{red}{2}} = \frac{14}{\textcolor{red}{2}}$

$y = 7$ or $\left(- 1 , 7\right)$

We can next plot the two points on the coordinate plane:

graph{((x-1)^2+(y+2)^2-0.125)((x+1)^2+(y-7)^2-0.125)=0 [-20, 20, -10, 10]}

Now, we can draw a straight line through the two points to graph the line:

graph{(9x+2y-5)((x-1)^2+(y+2)^2-0.125)((x+1)^2+(y-7)^2-0.125)=0 [-20, 20, -10, 10]}