What Is The Solution To The Equation Mc012-1.Jpg?

Introduction

As a professional teacher, it is my duty to ensure that students understand the concepts they are learning. Solving equations is an essential skill in mathematics, and one of the most common types of equations that students encounter is linear equations. In this article, we will discuss how to find the solution to the equation mc012-1.jpg.

Understanding Linear Equations

A linear equation is an equation that can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The equation mc012-1.jpg is a linear equation in slope-intercept form.

Breaking Down the Equation

The equation mc012-1.jpg can be rewritten as y = -2x + 5. This means that the slope of the line is -2 and the y-intercept is 5. The y-intercept is the point where the line crosses the y-axis.

Graphing the Equation

One way to visualize the solution to the equation is to graph it on a coordinate plane. To do this, we can plot the y-intercept at (0, 5) and then use the slope to find additional points on the line. For example, if we move one unit to the right (in the positive x direction), we would move two units down (in the negative y direction) to get to the point (1, 3). We can continue this pattern to plot additional points on the line.

Using Algebraic Methods to Find the Solution

Another way to find the solution to the equation mc012-1.jpg is to use algebraic methods. To do this, we can isolate the variable (y) on one side of the equation by subtracting -2x from both sides. This gives us the equation y - (-2x) = 5.

Simplifying the Equation

We can simplify the equation by adding 2x to both sides, which gives us y = 2x + 5. This is the same equation we got earlier when we rewrote mc012-1.jpg in slope-intercept form.

Interpreting the Solution

The solution to the equation y = 2x + 5 is a set of ordered pairs (x, y) that make the equation true. For example, the point (1, 7) is a solution to the equation because when we substitute x = 1 and y = 7 into the equation, we get 7 = 2(1) + 5, which is true.

Conclusion

In conclusion, the solution to the equation mc012-1.jpg is y = -2x + 5. This equation represents a line with a slope of -2 and a y-intercept of 5. We can find the solution by graphing the equation or by using algebraic methods. The solution is a set of ordered pairs that make the equation true.