Graph the equation and identify the \( y \)-intercept. \( y=\frac{4}{3} x+2 \) Use the graphing tool on the right to graph the eq Click to The \( y \)-intercept is graph (Type an ordered pair.)

To identify the \( y \)-intercept of the equation \( y = \frac{4}{3}x + 2 \), follow these steps: 1. **Understanding the Equation:** The given equation is in the slope-intercept form: \[ y = mx + b \] where: - \( m \) is the slope - \( b \) is the \( y \)-intercept 2. **Identify the \( y \)-Intercept:** In the equation \( y = \frac{4}{3}x + 2 \): - The slope \( m = \frac{4}{3} \) - The \( y \)-intercept \( b = 2 \) 3. **\( y \)-Intercept as an Ordered Pair:** The \( y \)-intercept occurs where \( x = 0 \). Plugging this into the equation: \[ y = \frac{4}{3}(0) + 2 = 0 + 2 = 2 \] So, the \( y \)-intercept is at the point \( (0, 2) \). 4. **Graphing the Equation:** - **Plot the \( y \)-intercept:** Start by plotting the point \( (0, 2) \) on the graph. - **Use the Slope to Find Another Point:** The slope \( \frac{4}{3} \) means that for every 3 units you move to the right (positive \( x \)-direction), you move up 4 units. Starting from \( (0, 2) \), moving right 3 units to \( x = 3 \) and up 4 units leads to the point \( (3, 6) \). - **Draw the Line:** Connect these points with a straight line extending in both directions. Here's a simple representation: ``` y | | * | | | |________________ x 0 ``` *(In this diagram, the asterisk (*) represents the \( y \)-intercept at \( (0, 2) \).)* **Final Answer:** The \( y \)-intercept is \( \boxed{(0,\ 2)} \).