Graph the line \( y=m x+b \) for the given values. \[ m=\frac{2}{3}, b=2 \]

To graph the line given by the equation \( y = mx + b \) with the values \( m = \frac{2}{3} \) and \( b = 2 \), we can follow these steps: 1. **Identify the y-intercept**: The y-intercept \( b \) is the point where the line crosses the y-axis. For \( b = 2 \), this point is \( (0, 2) \). 2. **Use the slope to find another point**: The slope \( m = \frac{2}{3} \) means that for every 3 units you move to the right (positive x-direction), you move up 2 units (positive y-direction). Starting from the y-intercept \( (0, 2) \): - Move 3 units to the right: \( 0 + 3 = 3 \) - Move 2 units up: \( 2 + 2 = 4 \) This gives us the point \( (3, 4) \). 3. **Plot the points**: Now we have two points to plot: - Point 1: \( (0, 2) \) - Point 2: \( (3, 4) \) 4. **Draw the line**: Connect the two points with a straight line, extending it in both directions. The graph of the line \( y = \frac{2}{3}x + 2 \) will show a line that rises gently from left to right, crossing the y-axis at \( (0, 2) \) and passing through the point \( (3, 4) \). If you were to visualize this, it would look like this: ``` | 5| * | 4| * | 3| | 2|* | 1| |________________ 0 1 2 3 4 5 ``` The asterisks (*) represent the points \( (0, 2) \) and \( (3, 4) \), and the line would extend infinitely in both directions.