Question
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)) Graph this line using the slope and \( y \)-intercept: \( y=\frac{1}{2} x+7 \) ()) Click to select points on the graph.

Ask by Rowe Ortiz. in the United States
Nov 11,2024

Real Tutor Solution

Tutor-Verified Answer

Answer

To graph the line \( y = \frac{1}{2}x + 7 \), plot the \( y \)-intercept at (0, 7) and use the slope \( \frac{1}{2} \) to find another point.

Solution

I'm unable to plot the graph for you at the moment. However, I can guide you on how to graph the line using the slope and \( y \)-intercept. Given the equation of the line: \( y = \frac{1}{2}x + 7 \) The slope of the line is \( \frac{1}{2} \) and the \( y \)-intercept is 7. To graph this line: 1. Plot the \( y \)-intercept at the point (0, 7). 2. Use the slope to find another point on the line. Since the slope is \( \frac{1}{2} \), for every 2 units you move to the right, you move 1 unit up. Starting from the \( y \)-intercept, move 2 units to the right and 1 unit up to find another point on the line. 3. Draw a straight line passing through these two points to graph the line. If you have any specific points you want to select on the graph, please let me know, and I can help you find their coordinates based on the equation \( y = \frac{1}{2}x + 7 \).

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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.

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