Pregunta
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Graph the following features: - Slope \( =-2 \) - Y-intercept \( =3 \)

Ask by George Schmidt. in the United States
Feb 24,2025

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To graph the line with a slope of –2 and a y-intercept of 3, plot the point (0, 3) and another point using the slope (1, 1), then draw a straight line through them.

Solución

To graph a line with a slope of –2 and a y-intercept of 3, follow these steps: 1. Write the equation in slope-intercept form: y = mx + b.   Here, m = –2 and b = 3, so the equation is y = –2x + 3. 2. Plot the y-intercept (0, 3) on the graph. This is the point where the line crosses the y-axis. 3. Use the slope to find another point. Since the slope –2 means "for every 1 unit you move to the right, move 2 units down":   - Starting from (0, 3), move 1 unit right to x = 1.   - Then move 2 units down: y = 3 - 2 = 1.   Now you have the point (1, 1). 4. Plot the point (1, 1). 5. Draw a straight line through the points (0, 3) and (1, 1), and extend it in both directions. Your graph now represents the line with a slope of –2 and a y-intercept of 3, which is the line defined by y = –2x + 3.

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Extra Insights

To graph the line with a slope of -2 and a y-intercept of 3, start by plotting the y-intercept at the point (0, 3) on the y-axis. From there, use the slope to determine the next points: for every 1 unit you move to the right (positive direction on the x-axis), move down 2 units (negative direction on the y-axis). This will give you the next point at (1, 1). Continuing this, you can plot additional points like (2, -1) to ensure you have a straight line. Finally, draw a line through these points to complete the graph! Remember, the slope tells you the steepness and direction of the line. A negative slope indicates that the line goes down as you move to the right, just like a slide! So get ready to enjoy the thrill of graphing—it's all about connecting the dots, just like in a fun puzzle game!

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