Determine whether the equation is linear or not. Then graph the equation by finding and plotting ordered-pair solutions. \( y=\frac{1}{6} x-1 \)

To determine whether the equation \( y = \frac{1}{6} x - 1 \) is linear, we can analyze its form. The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In this case: - The slope \( m = \frac{1}{6} \) - The y-intercept \( b = -1 \) Since it can be expressed in this form, the equation is indeed linear. ### Finding Ordered-Pair Solutions To graph the equation, we can find some ordered-pair solutions (x, y) by choosing different values for \( x \) and calculating the corresponding \( y \). 1. **When \( x = 0 \)**: \[ y = \frac{1}{6}(0) - 1 = -1 \] Ordered pair: \( (0, -1) \) 2. **When \( x = 6 \)**: \[ y = \frac{1}{6}(6) - 1 = 1 - 1 = 0 \] Ordered pair: \( (6, 0) \) 3. **When \( x = 12 \)**: \[ y = \frac{1}{6}(12) - 1 = 2 - 1 = 1 \] Ordered pair: \( (12, 1) \) 4. **When \( x = -6 \)**: \[ y = \frac{1}{6}(-6) - 1 = -1 - 1 = -2 \] Ordered pair: \( (-6, -2) \) ### Summary of Ordered-Pair Solutions - \( (0, -1) \) - \( (6, 0) \) - \( (12, 1) \) - \( (-6, -2) \) ### Graphing the Equation To graph the equation, plot the ordered pairs on a coordinate plane: 1. Plot the point \( (0, -1) \). 2. Plot the point \( (6, 0) \). 3. Plot the point \( (12, 1) \). 4. Plot the point \( (-6, -2) \). After plotting these points, draw a straight line through them, as the equation is linear. ### Conclusion The equation \( y = \frac{1}{6} x - 1 \) is linear, and we have found several ordered-pair solutions to help graph it. The graph will be a straight line with a slope of \( \frac{1}{6} \) and a y-intercept at \( -1 \).