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

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UpStudy AI · Accepted Answer

Function by following steps:
- step0: Find the y-intercept:
  $$y=-\frac{2}{5}x+3$$
- step1: Set $$x$$=0$$:$$
  $$y=-\frac{2}{5}\times 0+3$$
- step2: Multiply:
  $$y=0+3$$
- step3: Remove 0:
  $$y=3$$
Analyze the slope of the function $$ y=-\frac{2}{5} x+3 $$
Function by following steps:
- step0: Find the slope:
  $$y=-\frac{2}{5}x+3$$
- step1: Identify the slope:
  $$m=-\frac{2}{5}$$
To analyze the equation $$ y = -\frac{2}{5} x + 3 $$, we can extract the following key features:

1. **Y-Intercept**: The y-intercept occurs when $$ x = 0 $$. From the equation, we find:
   $$
   y = 3
   $$
   This means the graph intersects the y-axis at the point $$ (0, 3) $$.

2. **Slope**: The slope $$ m $$ of the line is given by the coefficient of $$ x $$:
   $$
   m = -\frac{2}{5}
   $$
   This indicates that for every 5 units you move to the right (positive direction along the x-axis), the line moves down 2 units (negative direction along the y-axis).

### Graph Characteristics:
- The line will slope downwards from left to right due to the negative slope.
- It will cross the y-axis at $$ (0, 3) $$.

### Conclusion:
The correct graph for the equation $$ y = -\frac{2}{5} x + 3 $$ will show a downward sloping line that intersects the y-axis at the point $$ (0, 3) $$.
The correct graph is a downward-sloping line that crosses the y-axis at (0, 3).

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

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