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Step 2 of 2: Determine the graph of the line with the given \( y \)-Intercept and slope. Answer 2 Points The point given for the \( y \)-intercept, \( (0,-4) \), is marked on the graph. Points can be moved by dragging or using the arrow keys. Any lines or curves will be drawn on whenever a point is moved.

Ask by Mann Gibbs. in the United States
Mar 03,2025

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Answer

To graph the line with a y-intercept at (0, -4) and a given slope, follow these steps: 1. Start at the y-intercept point (0, -4). 2. Use the slope to find another point. For example, with a slope of ½, move 2 units right and 1 unit up to reach (2, -3). 3. Plot the second point (2, -3). 4. Draw a straight line through both points, extending it in both directions. This line represents the equation y = (½)x – 4.

Solution

One correct method is to use the y‐intercept and the slope to plot a second point and then draw the line through both points. For example, suppose the given slope is ½. Then you can do the following: 1. Start at the given y‑intercept, (0, –4). This is where your line crosses the y‑axis. 2. Recall that “slope = rise/run” tells you how many units to move up (or down) and right (or left) to get to the next point. With a slope of ½, “rise” is 1 and “run” is 2. 3. From (0, –4), move 2 units to the right (increasing x by 2) and 1 unit upward (increasing y by 1) to get the point (2, –3). 4. Plot the point (2, –3) on the graph. 5. Draw a straight line through the points (0, –4) and (2, –3). Extend the line in both directions. This line is the graph of the equation y = (½)x – 4. (If your slope is different from ½, use its rise and run in the same way.)

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To draw the line with the given information, remember that the slope tells you how steep the line is and in which direction it goes. If your slope is positive, the line will rise from left to right, whereas if it’s negative, it will fall. Starting from your \( y \)-intercept point \( (0, -4) \), use the slope to find another point. For example, a slope of 2 means you move up 2 units and to the right 1 unit from your intercept. Mark that new point and simply connect the two with a straight line! A common mistake when plotting lines is forgetting that the slope is a ratio. It can be expressed differently; for instance, a slope of \( \frac{3}{2} \) means go up 3 units for every 2 units right. Remember to always keep the slope ratio in mind, and make sure your points reflect that movement accurately!

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