graph 2x y 5

Guri Bee

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20-10-2024

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Graphing 2x + y = 5: A Step-by-Step Guide

The equation 2x + y = 5 represents a straight line. Let's explore how to graph this line using different techniques.

Understanding the Equation

This equation is in the standard form of a linear equation: Ax + By = C, where A, B, and C are constants.

Method 1: Using Intercepts

• X-intercept: The x-intercept is the point where the line crosses the x-axis. At this point, y = 0. To find the x-intercept, substitute y = 0 into the equation:

  2x + 0 = 5 2x = 5 x = 5/2

  Therefore, the x-intercept is (5/2, 0).

• Y-intercept: The y-intercept is the point where the line crosses the y-axis. At this point, x = 0. To find the y-intercept, substitute x = 0 into the equation:

  0 + y = 5 y = 5

  Therefore, the y-intercept is (0, 5).

• Plotting the Intercepts: Plot the points (5/2, 0) and (0, 5) on the coordinate plane.

• Drawing the Line: Connect the two plotted points with a straight line. This line represents the graph of the equation 2x + y = 5.

Method 2: Using Slope-Intercept Form

• Rearranging the Equation: We can rewrite the equation 2x + y = 5 in slope-intercept form (y = mx + c), where 'm' is the slope and 'c' is the y-intercept.

  y = -2x + 5

• Identifying Slope and Y-intercept: From the slope-intercept form, we can see that the slope is -2 and the y-intercept is 5.

• Plotting the Y-intercept: Plot the point (0, 5) on the coordinate plane.

• Using the Slope: The slope -2 indicates that for every 1 unit move to the right, the line moves 2 units down. Starting from the y-intercept, move 1 unit right and 2 units down to find another point on the line.

• Drawing the Line: Connect the two plotted points with a straight line. This line represents the graph of the equation 2x + y = 5.

Let's Summarize!

• The graph of 2x + y = 5 is a straight line.
• You can graph the line by finding its x and y intercepts, or by rewriting the equation in slope-intercept form.
• Both methods provide the same graph, making it easier to visualize the relationship between x and y in the equation.

Example Applications:

This equation can represent various real-world scenarios, like the cost of buying apples and oranges at a specific price. For example:

• Let 'x' represent the number of apples and 'y' represent the number of oranges.
• If apples cost $2 each and oranges cost $1 each, and you have $5 to spend, the equation 2x + y = 5 would model your spending.

By graphing this equation, you can see different combinations of apples and oranges you can buy within your budget.

Remember:

• Always label the axes (x and y) and the points plotted on the graph.
• Use a ruler or straight edge to ensure a precise line.

Sources:

• Graphing Linear Equations in Standard Form
• Graphing Linear Equations Using Intercepts

This article provided a detailed guide to graphing the linear equation 2x + y = 5 using different methods. By understanding these techniques, you can effectively visualize and analyze linear relationships in various real-world contexts.