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Standard Form

Sep 15, 2022
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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. 
Understand Standard Form of a Linear Equation 
Understand Standard Form of a Linear Equation 

Solution: 

x = cost of T-shirts 

y = blanket wraps 

blanket wrap sum

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

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

parallel

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. 
slope intercept form

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. 

bread

Solution: 

x = bread cost 

parallel

y = rolls cost 

rolls

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) 

graph

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). 

graph

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

Concept Map

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

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