Short Answer 
The equation y + 3 = 2(x + 3) represents a linear relationship. By rearranging it to y = 2x + 3, we determine the slope as 2 and the y-intercept at 3, allowing us to plot key points for graphing the line.
Step 1: Understanding the Equation
The equation given is y + 3 = 2(x + 3). To effectively create a graph, it is crucial to first understand this equation and its components. This equation presents a linear relationship, indicating how y depends on x. Specifically, the goal is to express this equation in the slope-intercept form, y = mx + b, where m represents the slope and b is the y-intercept.
Step 2: Solving the Equation
By rearranging the equation, you can isolate y to identify its slope and intercepts. Follow these steps to solve:
- Start from y + 3 = 2(x + 3).
- Simplify to y = 2x + 6 – 3.
- This results in the final equation: y = 2x + 3, with a slope of 2 and y-intercept of 3.
Step 3: Graphing the Equation
With the final equation y = 2x + 3, you can now plot the graph. The key points to remember for graphing include:
- The y-intercept is at (0, 3), where the line crosses the y-axis.
- The slope of 2 means that for every unit moved to the right (1 unit in x), you move 2 units up (in y).
- Two points to plot include (-3, -3) and (0, 3), which will help define the line accurately.