Determine whether the equation is linear or not. Then graph the equation by finding and plotting ordered-pair solutions. \( y=8 x \)

To determine whether the equation \( y = 8x \) is linear, we can analyze its form. The equation is in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In this case: - The slope \( m = 8 \) - The y-intercept \( b = 0 \) Since it can be expressed in this form, the equation \( y = 8x \) is indeed a linear equation. ### Finding Ordered-Pair Solutions To graph the equation, we can find some ordered pairs (x, y) by choosing different values for \( x \) and calculating the corresponding \( y \). 1. **When \( x = -2 \)**: \[ y = 8(-2) = -16 \quad \Rightarrow \quad (-2, -16) \] 2. **When \( x = -1 \)**: \[ y = 8(-1) = -8 \quad \Rightarrow \quad (-1, -8) \] 3. **When \( x = 0 \)**: \[ y = 8(0) = 0 \quad \Rightarrow \quad (0, 0) \] 4. **When \( x = 1 \)**: \[ y = 8(1) = 8 \quad \Rightarrow \quad (1, 8) \] 5. **When \( x = 2 \)**: \[ y = 8(2) = 16 \quad \Rightarrow \quad (2, 16) \] ### Ordered Pairs The ordered pairs we found are: - (-2, -16) - (-1, -8) - (0, 0) - (1, 8) - (2, 16) ### Graphing the Equation To graph the equation, plot the ordered pairs on a coordinate plane: 1. Plot the point (-2, -16). 2. Plot the point (-1, -8). 3. Plot the point (0, 0). 4. Plot the point (1, 8). 5. Plot the point (2, 16). After plotting these points, draw a straight line through them, as they all lie on the same line, confirming that the equation is linear. ### Conclusion The equation \( y = 8x \) is linear, and we can graph it using the ordered pairs we calculated. The graph will be a straight line passing through the origin (0, 0) with a slope of 8.