Select the correct graph for the equation below: \( y=-\frac{2}{5} x+3 \)

To determine the correct graph for the equation \( y = -\frac{2}{5} x + 3 \), we can analyze the equation step by step. 1. **Identify the slope and y-intercept:** - The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. - Here, the slope \( m = -\frac{2}{5} \) and the y-intercept \( b = 3 \). 2. **Plot the y-intercept:** - The y-intercept is the point where the line crosses the y-axis. For this equation, it is at the point \( (0, 3) \). 3. **Use the slope to find another point:** - The slope \( -\frac{2}{5} \) means that for every 5 units you move to the right (positive x-direction), you move down 2 units (negative y-direction). - Starting from the y-intercept \( (0, 3) \): - Move 5 units to the right to \( (5, 3) \). - Then move down 2 units to \( (5, 1) \). - So another point on the line is \( (5, 1) \). 4. **Draw the line:** - Now, you can plot the points \( (0, 3) \) and \( (5, 1) \) on a graph and draw a straight line through them. 5. **Characteristics of the graph:** - The line will slope downwards from left to right due to the negative slope. With this analysis, you can now select the graph that shows a line passing through the points \( (0, 3) \) and \( (5, 1) \) with a downward slope.