21. Graph \( y=-\frac{1}{2} x+2 \). Is \( (2,1) \) a solution?

1. **Graph \( y = -\frac{1}{2}x + 2 \):** - The equation is in slope-intercept form \( y = mx + b \) where the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = 2 \). - **Plot the y-intercept:** Start by plotting the point \( (0,2) \) on the graph. - **Use the slope:** The slope \( -\frac{1}{2} \) means that for every 2 units you move to the right, you move 1 unit down. From \( (0,2) \), moving 2 units right to \( (2,2) \) leads to moving 1 unit down to \( (2,1) \). - **Draw the line:** Plot several points using the slope, then draw a straight line through these points. 2. **Check if \( (2,1) \) is a solution:** - Substitute \( x = 2 \) and \( y = 1 \) into the equation: \[ 1 = -\frac{1}{2}(2) + 2 \] - Calculate: \[ 1 = -1 + 2 \] \[ 1 = 1 \] - The equation holds true. \[ \textbf{Conclusion: } (2,1) \text{ is a solution to the equation.} \]