Math Problem Statement

Graph y=-2x+3

Solution

To graph the equation y=2x+3y = -2x + 3, follow these steps:

  1. Identify the slope and y-intercept:

    • The slope (mm) is 2-2, which means for every 1 unit increase in xx, yy decreases by 2 units.
    • The y-intercept (bb) is 33, which means the line crosses the y-axis at the point (0,3)(0, 3).
  2. Plot the y-intercept:

    • Start by plotting the point (0,3)(0, 3) on the graph.
  3. Use the slope to find another point:

    • From the y-intercept (0,3)(0, 3), move 1 unit to the right (increase xx by 1) and 2 units down (since the slope is 2-2), landing at the point (1,1)(1, 1).
    • Plot this point (1,1)(1, 1) on the graph.
  4. Draw the line:

    • Draw a straight line through the points (0,3)(0, 3) and (1,1)(1, 1). This line is the graph of the equation y=2x+3y = -2x + 3.

Would you like a detailed image of the graph?


Here are 5 relative questions to consider:

  1. How would the graph change if the slope was positive?
  2. What happens to the graph if the y-intercept changes to -3?
  3. How would you graph y=2x+3y = 2x + 3, and how does it differ from y=2x+3y = -2x + 3?
  4. How can you determine the x-intercept of the line y=2x+3y = -2x + 3?
  5. How would the graph look if the equation were y=2xy = -2x (no y-intercept)?

Tip: When graphing, always start with the y-intercept and use the slope to find other points on the line for accuracy.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9