Final answer:
In order to graph the equation y - 3 = -2/3x + 6, plot the y-intercept (0, 9) and use the slope of -2/3 to find additional points. Then, connect the points to draw the line on the graph.
Step-by-step explanation:
To graph the equation y - 3 = -2/3x + 6, we can follow these steps:
1. Rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Start by isolating y on one side of the equation:
y = -2/3x + 6 + 3
Simplify the equation:
y = -2/3x + 9
2. Identify the slope and y-intercept from the equation.
The slope, represented by m, is -2/3.
The y-intercept, represented by b, is 9.
3. Plot the y-intercept on the graph.
Locate the point (0, 9) on the y-axis. This represents the y-intercept.
4. Use the slope to find additional points on the line.
- The slope of -2/3 means that for every 3 units moved horizontally (x-axis), the corresponding y-value moves 2 units downwards.
- Starting from the y-intercept (0, 9), move 3 units to the right and 2 units down to find another point on the line. This gives us the point (3, 7).
- Repeat this process to find more points if needed.
5. Connect the points on the graph.
Once you have enough points, use a straight edge or ruler to draw a line passing through them. This line represents the graph of the equation.