The problem requires simplifying the linear equation $7x + y + 3 = 9x$ and then graphing the simplified equation.

1. Problem Description

The problem requires simplifying the linear equation $7x + y + 3 = 9x$ and then graphing the simplified equation.

2. Solution Steps

First, we simplify the equation $7x + y + 3 = 9x$.

Subtract $7x$ from both sides of the equation:

$7x + y + 3 - 7x = 9x - 7x$

$y + 3 = 2x$

Subtract 3 from both sides of the equation:

$y + 3 - 3 = 2x - 3$

$y = 2x - 3$

This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Here, the slope $m = 2$ and the y-intercept $b = -3$.

To graph this line, we need at least two points.

We can use the y-intercept $(0, -3)$ as one point.

To find another point, we can choose a value for $x$ and solve for $y$. Let $x = 1$.

$y = 2(1) - 3 = 2 - 3 = -1$

So, the point $(1, -1)$ is on the line.

3. Final Answer

$y = 2x - 3$