\[ y=-\frac{1}{6} x+5 \] Click to select points on the graph.

The equation you provided is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. For the equation \( y = -\frac{1}{6}x + 5 \): - The slope \( m = -\frac{1}{6} \) indicates that for every 6 units you move to the right (positive x-direction), the value of \( y \) decreases by 1 unit. - The y-intercept \( b = 5 \) means that the line crosses the y-axis at the point (0, 5). To find specific points on the graph, you can choose different values for \( x \) and calculate the corresponding \( y \) values. Here are a few examples: 1. **When \( x = 0 \)**: \[ y = -\frac{1}{6}(0) + 5 = 5 \] Point: \( (0, 5) \) 2. **When \( x = 6 \)**: \[ y = -\frac{1}{6}(6) + 5 = -1 + 5 = 4 \] Point: \( (6, 4) \) 3. **When \( x = 12 \)**: \[ y = -\frac{1}{6}(12) + 5 = -2 + 5 = 3 \] Point: \( (12, 3) \) 4. **When \( x = -6 \)**: \[ y = -\frac{1}{6}(-6) + 5 = 1 + 5 = 6 \] Point: \( (-6, 6) \) 5. **When \( x = -12 \)**: \[ y = -\frac{1}{6}(-12) + 5 = 2 + 5 = 7 \] Point: \( (-12, 7) \) You can plot these points on a graph to visualize the line represented by the equation. The line will slope downwards from left to right due to the negative slope.