Y Value When X = -3 In Y = 2X + 1: Step-by-Step Solution

Hey guys! Today, we're diving into a fundamental concept in algebra: evaluating equations. Specifically, we're going to figure out the value of Y when X is -3 in the equation Y = 2X + 1. This is a common type of problem you'll encounter in your math journey, so let's break it down step-by-step. We'll explore the equation, understand the process of substitution, solve for Y, and then discuss the correct answer and why the other options are incorrect. Think of it as a math adventure, where we're detectives uncovering the mystery of Y! This is more than just finding an answer; it's about grasping the underlying principles of algebraic equations. Understanding how to substitute values and solve for unknowns is crucial for more advanced mathematical concepts. So, let’s put on our thinking caps and get started on this exciting mathematical exploration!

Breaking Down the Equation: Y = 2X + 1

Before we jump into solving for Y, let's take a moment to understand what the equation Y = 2X + 1 actually means. In simple terms, this equation describes a relationship between two variables, X and Y. Think of it as a mathematical recipe: if you give me a value for X, I can use this equation to tell you the corresponding value for Y. The equation is in slope-intercept form, which is a common way to represent linear equations. The '2' in front of the 'X' represents the slope of the line, indicating how much Y changes for every unit change in X. The '+ 1' represents the y-intercept, which is the point where the line crosses the y-axis. Understanding these components helps us visualize the equation as a straight line on a graph. Each point on this line represents a pair of X and Y values that satisfy the equation. The process of substituting a value for X and solving for Y is like finding a specific point on this line. So, when we're asked to find the value of Y when X = -3, we're essentially asking, "What is the y-coordinate of the point on this line where the x-coordinate is -3?" This connection between equations and their graphical representations is a powerful tool in mathematics, allowing us to visualize and understand abstract concepts more easily.

The Magic of Substitution: Plugging in X = -3

Now comes the fun part: substitution! This is where we replace the variable X in the equation with its given value, which is -3 in this case. So, we take our equation, Y = 2X + 1, and wherever we see an X, we put a -3 in its place. It's like we're swapping out the letter X for the number -3. But it's crucial to do it carefully, making sure we maintain the integrity of the equation. This gives us a new equation: Y = 2 * (-3) + 1. Notice how we've replaced the X with (-3), keeping the multiplication and addition operations intact. The parentheses around the -3 are important because they clearly indicate that we're multiplying 2 by -3, rather than subtracting 3. Substitution is a fundamental technique in algebra and beyond. It allows us to evaluate expressions, solve equations, and even define functions. It's like having a master key that unlocks the value of an expression for a specific input. By substituting, we transform a general equation into a specific calculation, bringing us one step closer to our answer. It’s like plugging in the coordinates into a map to find a specific location. Once we perform the substitution, the equation becomes a simple arithmetic problem that we can easily solve.

Solving for Y: Step-by-Step

With X substituted, we now have Y = 2 * (-3) + 1. To solve for Y, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, we handle the multiplication: 2 * (-3) equals -6. So our equation becomes Y = -6 + 1. Now, we simply add -6 and 1. Remember that adding a negative number is the same as subtracting. So, -6 + 1 is the same as 1 - 6, which equals -5. Therefore, we've found that Y = -5. Each step in this process is like a piece of a puzzle, and when we put them together correctly, they reveal the solution. This step-by-step approach is crucial for accuracy and helps prevent errors. It's like carefully constructing a building, making sure each brick is in its place before moving on to the next. Solving for Y is the climax of our mathematical journey, the point where we reveal the unknown. By following the order of operations and performing the calculations meticulously, we arrive at the solution with confidence.

The Answer and Why Others Don't Fit

We've crunched the numbers and discovered that when X = -3 in the equation Y = 2X + 1, the value of Y is -5. So, the correct answer is A) -5. But why are the other options incorrect? Let's take a look. If we were to substitute X = -3 into the equation and mistakenly perform the addition before the multiplication, we might arrive at an incorrect answer. For example, if we added 2 and 1 first, we'd get 3, and then multiplying by -3 would give us -9, which isn't one of the options but highlights the importance of order of operations. The other options, B) -7, C) -6, and D) -4, are incorrect because they don't satisfy the equation when X = -3. If you were to plug these values back into the original equation, you wouldn't get a true statement. For instance, if Y were -7, the equation would become -7 = 2*(-3) + 1, which simplifies to -7 = -6 + 1, or -7 = -5, which is false. Understanding why the incorrect options are wrong reinforces our understanding of the correct process and the importance of each step. It's like learning to distinguish between a genuine painting and a forgery; by understanding the flaws in the forgery, we appreciate the authenticity of the original even more. By eliminating the incorrect answers, we solidify our understanding of the correct solution and the underlying mathematical principles.

Wrapping Up: Mastering Algebraic Equations

So, guys, we've successfully navigated this algebraic equation and found that when X = -3 in the equation Y = 2X + 1, Y equals -5. We've covered the importance of understanding the equation, the magic of substitution, the step-by-step process of solving for Y, and why the other options just don't fit. But more importantly, we've reinforced some fundamental concepts in algebra that will serve you well in your future math endeavors. Remember, equations are like puzzles, and with the right tools and techniques, we can solve them! Practice makes perfect, so keep working on these types of problems, and you'll become a master of algebraic equations in no time. Think of this as just one step in a much larger mathematical journey. The skills you've gained here, like substitution and solving for variables, are building blocks for more advanced topics like graphing, systems of equations, and even calculus. So, embrace the challenge, keep asking questions, and never stop exploring the wonderful world of mathematics! And remember, math isn't just about finding the right answer; it's about the journey of discovery and the satisfaction of understanding how things work. Keep up the great work, guys!