Understanding The Graph Of 2X - 3Y = 3

SOLUTION graph 2x3y=3 from www.algebra.com

Introduction

In mathematics, a graph is a visual representation of a mathematical equation or function. It helps us understand the behavior and relationship between two variables. The graph of 2x - 3y = 3 is a straight line that passes through the x and y-axis. In this article, we will discuss how to graph this equation and its properties.

Graphing the Equation

To graph the equation 2x - 3y = 3, we need to find at least two points on the line. One way to do this is to rearrange the equation in terms of y: 2x - 3y = 3 -3y = -2x + 3 y = (2/3)x - 1 Now we can choose any two x-values and substitute them into the equation to find the corresponding y-values. For example, if we choose x = 0 and x = 3, we get: y = (2/3)(0) - 1 = -1 and y = (2/3)(3) - 1 = 1 So the two points on the line are (0, -1) and (3, 1). We can now plot these points and draw a straight line that passes through them.

Properties of the Graph

The graph of 2x - 3y = 3 is a straight line with a slope of 2/3. This means that for every increase of 2 in the x-value, the y-value increases by 3. Similarly, for every decrease of 2 in the x-value, the y-value decreases by 3. The y-intercept of the line is -1, which means that the line crosses the y-axis at (0, -1). The x-intercept can be found by setting y = 0: 2x - 3(0) = 3 2x = 3 x = 3/2 So the x-intercept is (3/2, 0).

Using the Graph to Solve Equations

The graph of 2x - 3y = 3 can also be used to solve equations involving x and y. For example, if we want to find the solution to the equation 2x - 3y = 9, we can start by plotting the line for the equation 2x - 3y = 3. Next, we can draw a parallel line to this line that passes through the point (0, 3). This is because both lines have the same slope of 2/3. The intersection point of these two lines is the solution to the equation 2x - 3y = 9, which is (6, 0).

Conclusion

In conclusion, the graph of 2x - 3y = 3 is a straight line with a slope of 2/3. It passes through the points (0, -1) and (3, 1) and crosses the y-axis at (0, -1) and the x-axis at (3/2, 0). The graph can also be used to solve equations involving x and y. Understanding the properties of this graph can help us understand the behavior and relationship between two variables.