Understanding The Graph Of 4X 2Y 3

Which is the graph of 4x+2y from brainly.com

Introduction

When we think about graphs, we often picture a set of coordinates that are plotted on a graph paper. These coordinates are essential for representing mathematical equations and formulas in a visual way. In this article, we will look at the graph of 4x 2y 3 and understand what it represents and how to solve it.

Defining the Equation

The equation 4x 2y 3 represents a linear equation in two variables, x and y, where 4 is the coefficient of x and 2 is the coefficient of y. The constant 3 is added to the equation. When we plot this equation on a graph, we will get a straight line, and every point on this line will satisfy the equation.

Understanding the Cartesian Plane

Before we proceed to plot the graph, we need to understand the Cartesian plane. The Cartesian plane is a two-dimensional plane that consists of two axes, the x-axis, and the y-axis. The x-axis is horizontal, and the y-axis is vertical, and both intersect at the origin (0,0).

Plotting the Graph

To plot the graph of 4x 2y 3, we need to find at least two points that satisfy the equation. We can do this by substituting some values of x and solving for y. Let's assume x = 1, then the equation becomes 4(1) 2y 3, which simplifies to 2y -1. Solving for y, we get y = 2. We can also assume x = 2, then the equation becomes 4(2) 2y 3, which simplifies to 2y -2. Solving for y, we get y = 2.5. Now we have two points, (1,2) and (2,2.5), that satisfy the equation. We can plot these points on the Cartesian plane and draw a straight line that passes through them.

Understanding the Slope and Intercept

The slope of a line is a measure of its steepness and is given by the formula, m = (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are any two points on the line. The slope of the line 4x 2y 3 is -2, which means that for every unit increase in x, y will decrease by 2. The y-intercept of a line is the point where it intersects the y-axis. To find the y-intercept of the line 4x 2y 3, we need to substitute x = 0 in the equation, which gives us 2y = 3, and y = 1.5.

Graphical Representation

We can represent the graph of 4x 2y 3 in a graphical form using software like Microsoft Excel or Grapher. We can input the equation in the software and generate a graph that shows the line passing through the points (1,2) and (2,2.5).

Real-Life Applications

Linear equations like 4x 2y 3 have numerous real-life applications, including calculating the cost of production, understanding the relationship between two variables, and predicting the trend in financial markets.

Conclusion

In conclusion, the graph of 4x 2y 3 is a straight line that passes through the points (1,2) and (2,2.5). It has a slope of -2 and a y-intercept of 1.5. Understanding linear equations and their graphs is crucial in solving real-life problems and making informed decisions.