https://file.aiquickdraw.com/mathbot/file/1725794876039dtbp2nw0.jpg

Let's break down and analyze the math problems presented in the image:

### Section 1: Coefficient and Constant
- **What is the coefficient of y?**
  - The answer provided is **1**. This means that the term involving \( y \) is just \( y \), implying the coefficient is 1.
  
- **What is the constant?**
  - The constant is **4**.

### Section 2: Algebraic Expressions from Word Descriptions
- **The sum of \( a \) and \( b \)** is represented as **ab**, but this seems incorrect as "sum" should indicate addition, not multiplication. It should likely be written as **a + b**.
  
- **5 less than \( y \)** is correctly written as \( y - 5 \).
  
- **The product of \( x \) and \( y \)** is correctly written as **xy**.

- **Triple \( c \) divided by \( d \)** is correctly written as \( \frac{3c}{d} \).

### Section 3: Substituting Numbers into Expressions
Given \( x = 2 \) and \( y = 3 \):

- **\( -x + y \)**: 
  - Substitution yields \( -2 + 3 = 1 \).
  
- **\( xy \)**: 
  - Substitution yields \( 2 \times 3 = 6 \).

- **\( 2y + x \)** divided by 2:
  - Substitution yields \( \frac{2(3) + 2}{2} = \frac{6 + 2}{2} = \frac{8}{2} = 4 \).

- **\( \sqrt{x^2 + 7y} \)**:
  - Substitution yields \( \sqrt{2^2 + 7(3)} = \sqrt{4 + 21} = \sqrt{25} = 5 \).

---

Would you like any further clarification or details on any of the sections? Here are some follow-up questions to consider:

1. Can you explain how to identify the coefficient and constant in a linear equation?
2. Why should the sum of two numbers be represented by addition rather than multiplication?
3. What is the general formula for evaluating an expression after substituting values?
4. How does the square root operation apply in the final expression?
5. Can you write out other algebraic expressions based on different word descriptions?

**Tip**: When substituting values into an expression, always follow the order of operations (PEMDAS) to ensure accuracy.

What is the coefficient of y? What is the constant? Write algebraic expressions from word descriptions, substitute numbers for variables, and evaluate.

Learn how to identify coefficients and constants in algebraic expressions, write expressions from word descriptions, and substitute values for variables to evaluate expressions. This guide provides a detailed breakdown of basic algebraic concepts suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation