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

To graph the equation \( y = -\frac{1}{2}x + 2 \), start by plotting the y-intercept at (0, 2). Then, from there, use the slope of -1/2 to find another point: go down 1 unit and right 2 units, landing at (2, 1). Now, to check if (2, 1) is a solution, substitute \( x = 2 \) into the equation: \[ y = -\frac{1}{2}(2) + 2 = -1 + 2 = 1. \] Since the result equals the y-coordinate of the point (2, 1), yes, (2, 1) is indeed a solution! Remember, to double-check your work, always substitute the point into the original equation. It's a foolproof way to confirm if your points are correct! Also, a common mistake is to overlook the slope's direction—ensure you're moving down for negative slopes.