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Chapter 3: Problem 1

Let \(y=2 x+1 .\) Find the value of \(y\) when. $$x=0$$

Short Answer

Expert verified
The value of y when x = 0 is 1.

Step by step solution

01

Substitute x with 0

Insert the value of \(x = 0\) into the equation. The equation becomes \(y = 2*0 + 1\).
02

Simplify

After substitution, simplify the equation. The 2 multiplied by 0 will become 0, so the equation is now \(y = 0 + 1\).
03

Final Calculation

The final step is to simplify \(y = 0 + 1\) which gives \(y = 1\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution
Substitution is a method used in algebra to replace a variable with a given value. It's a powerful tool to simplify equations and solve for unknowns. In our example, we have the equation \( y = 2x + 1 \). If we want to find the value of \( y \) when \( x = 0 \), we substitute the variable \( x \) in the equation with the value 0.
By replacing \( x \) with 0, the equation becomes \( y = 2 \times 0 + 1 \). This step of substitution is essential as it sets the stage for further simplification of the expression.
Remember, always ensure that you're substituting the correct values in place of the correct variables to prevent calculation errors.
Simplifying Expressions
Simplifying expressions involves rewriting them in a simpler or more compact form without changing their value. In our specific exercise, after substituting the value of \( x = 0 \) into the equation \( y = 2 \times 0 + 1 \), we simplify by performing the multiplication.
The multiplication \( 2 \times 0 \) results in 0, so the equation becomes \( y = 0 + 1 \). Simplification often follows substitution to make equations easier to interpret and solve.
  • Check if there are any terms that can be combined
  • Perform basic arithmetic operations to reduce complexity
  • Aim for the simplest form of the expression
Simplifying is achieving the cleanest and most direct form possible to make further calculations straightforward.
Arithmetic Operations
Arithmetic operations form the foundation of algebra. In our example, these operations include addition and multiplication. Once simplified to \( y = 0 + 1 \), we compute the operations.
Here's how they apply:
  • Multiplication: The expression \( 2 \times 0 \) is a multiplication operation, yielding 0. Multiplication by zero results in zero.
  • Addition: After multiplication, we then add 0 and 1 to get the final result of 1.
Understand that each arithmetic operation follows specific rules that help us carry out these calculations correctly. Always perform operations in their correct order to ensure accurate results.

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Most popular questions from this chapter

Express each inverse variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 2. (OBJECTIVE 2) varies inversely with \(x .\) If \(y=6\) when \(x=2,\) find \(y\) when \(x=4\).

Express each variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. \(b\) varies directly with \(c\) and inversely with \(d^{2}\). If \(b=5\) when \(c=2\) and \(d=4\), find \(b\) when \(c=36\) and \(d=2\).

Fill in the blanks. Assume that \(k\) is a constant. In the equation \(y=k x, k\) is called the _____ of variation.

Express each variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. \(c\) varies jointly with \(d\) and \(h .\) If \(c=196\) when \(d=6\) and \(h=4,\) find \(d\) when \(c=705.6\) and \(h=16\).

Graph each equation using any method. $$y=4.5 x+2$$
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