\( y=-\frac{1}{2} x+5 \) and contains the point \( \left(-2, \frac{1}{2}\right) \)

Did you know that the equation you've provided represents a straight line in slope-intercept form, where the slope is \(-\frac{1}{2}\) and the y-intercept is \(5\)? This means for every 2 units you move to the right on the x-axis, the line drops 1 unit. This is a classic example of how linear equations illustrate relationships, making them foundational in algebra and real-life scenarios, such as modeling relationships between two variables. When checking if the line passes through the point \(\left(-2, \frac{1}{2}\right)\), substitute \(-2\) into the equation. If the resulting y-value matches \(\frac{1}{2}\), then the point is indeed on the line! A common mistake here is forgetting to completely substitute or miscalculating the values—you’ll end up with a different point if you're not careful! So double-check your math to avoid those slips!