## Key Concepts

- Understand standard form of a linear equation
- Sketch the graph of a linear equation in standard form

## Understand Standard Form of a Linear Equation

- The Band Booster Club is selling T-shirts and blanket wraps to raise money for a trip. The band director has asked the club to raise $1000. The booster club president wants to know how many T-shirts and how many blanket wraps the club needs to sell to meet their goal of $1000. The T-shirts cost $10 each, and the blanket wraps cost $20 each. Write a linear equation in standard form that describes the problem.

**Solution: **

x = cost of T-shirts

y = blanket wraps

The equation 10x +20y = 1000 is in standard form.

The standard form of linear equation is Ax + By = C.

Where A, B and C are integers, and A and B are not both equal to zero

**Compare equivalent slope-intercept and standard forms for the situation in part A.**

**Example 2:**

A baker sells bread for $3 a loaf and rolls for $1 each. The baker needs to sell $24 worth of baked goods by the end of the day.

Solution:

x = bread cost

y = rolls cost

The equation 3x + y = 24 is in standard form.

### Sketch the Graph of a Linear Equation in Standard Form

**Example 1:**

Sketch the graph of 5y + 3x = 30 ?

**Sol:**

**Step1:**

To find the *y*-intercept, set x = 0 and solve for *y*.

5y + 3x = 30

5y + 3(0) = 30

5y + 0 = 30

5y = 30

y = 6

y-intercept (0, 6)

**Step2:**

5y + 3x = 30

5(0) + 3x = 30

0 +3x = 30

3x = 30

x = 10

x-intercept (10, 0)

**Example2:**

What is the graph of 3y + 2x = 6 ?

**Solution:**

**Step 1:**

3(0) + 2x = 6.

2x = 6

x = 3

The *x*-intercept is (3, 0)

**Step 2:**

The y-intercept occurs when x = 0.

y + 2(0) = 6

3y = 6

y = 2

The *y*-intercept is (0, 2).

## Exercise

- Your school sells adult and student tickets to a school play. Adult tickets cost $15 each and student tickets cost $4. The total value of all the tickets sold is $7000. The director is predicting 352 adult tickets will be sold; how many student tickets need to be sold to reach $7000? Write a linear equation in standard form that describes the problem and then solves it to answer the question.
- A test has some questions worth 2 points and some questions worth 4 points. The test is worth 100 points. Write an equation in standard form to represent the situation.
- I have $36 in 5 dollar bills and 1 dollar bill. Write an equation in standard form.
- Standard form of linear equation Ax + By = C. Where A, B, C are___________.
- You want to earn $1000 teaching children about how to swim. You earn $10 per hour for an individual instruction and $25 per hour for instructing groups. Write an equation in standard form.
- Identify the x-and y- intercepts to graph of the equation. 3x – 4y = 24.
- Sketch the graph of each equation: 3x – 6y = – 12
- Sketch the graph of each equation: 8x + 12y =- 24
- Sketch the graph of each equation: 3y – 2x= – 12
- Sketch the graph of each equation: 5x + 4y = 20

### Concept Map

### What have we learned

- Understand standard form of a linear equation
- Understand how to represent the situation with linear equation
- Sketch the Graph of a Linear Equation in Standard Form
- Finding x- intercept and y-intercept

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: