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# Standard Form

Sep 15, 2022

## 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

1. 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

1. 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:

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

1. 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.
2. 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.
3. I have \$36 in 5 dollar bills and 1 dollar bill. Write an equation in standard form.
4. Standard form of linear equation Ax + By = C. Where A, B, C are___________.
5. 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.
6. Identify the x-and y- intercepts to graph of the equation. 3x – 4y = 24.
7. Sketch the graph of each equation: 3x – 6y = – 12
8. Sketch the graph of each equation: 8x + 12y =- 24
9. Sketch the graph of each equation: 3y – 2x= – 12
10. Sketch the graph of each equation: 5x + 4y = 20

### 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

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