)) Graph this line using the slope and \( y \)-intercept: \( y=\frac{1}{2} x+7 \) ()) Click to select points on the graph.
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The Deep Dive
To graph the line \( y=\frac{1}{2} x+7 \), start by plotting the \( y \)-intercept. This plane cuts through the \( y \)-axis at \( (0, 7) \). Now, using the slope of \( \frac{1}{2} \), for every 2 units you move right on the \( x \)-axis, move up 1 unit on the \( y \)-axis. Plot another point at \( (2, 8) \) and connect the points to create a straight line. You can also reflect on how linear equations form the backbone of various real-life scenarios. For example, understanding this concept can help in predicting costs, tracking growth, or even analyzing trends in data, such as a company's sales over time! Once you master this graphing technique, you'll find it surprisingly useful in everyday life.