Using Equations in Standard and Slope Intercept Form

Slides:

Advertisements

Similar presentations

Objective The student will be able to:

Advertisements

Graph Linear Systems Written in Standard Form

CHAPTER V Writing Linear Equations

Finding the equation of a line.

Systems of Equations OBJECTIVES To understand what a system of equations is. Be able to solve a system of equations from graphing the equations Determine.

Math 015 Section 6.1 Equations. Many students like to remember the process for solving linear equations as: any algebra expressions on each side variable.

5.5 Standard Form of a Linear Equation

Write an equation given two points

Writing Equations of Lines Starting with Point – Slope Form y – y 1 = m (x – x 1 )

Section 6-3: Standard Form of a Linear Equation SPI 22C: select the graph that represents a given linear function Objective: Graph and write linear equations.

Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 3 Equations and Inequalities in Two Variables; Functions.

5.6 – Standard Form of a Linear Equation

Objective You will be able to: 1) write equations using slope-intercept form. 2) identify slope and y-intercept from an equation. 3) write equations in.

Daily Homework Quiz Review 5.3

The Multiplication Principle of Equality 2.3a 1.Solve linear equations using the multiplication principle. 2.Solve linear equations using both the addition.

5.5 Standard Form of a Linear Equation

Using linear equations to solve word problems

Bellwork Tuesday Bellwork Solutions

Solving Systems Using Elimination

5.2 Equations of Lines Given the Slope and a Point.

Understand linear equations and its types. Form the linear equations involving slopes of different situations. Students and Teachers will be able to.

EXAMPLE 1 Identify slope and y-intercept Identify the slope and y- intercept of the line with the given equation. y = 3x x + y = 22. SOLUTION The.

Ax + By = c.  The Standard Form for a linear equation in two variables, x and y, is usually given as Ax + By = C where, if at all possible, A, B, and.

Warm up Multiply or divide the given fraction make sure to reduce 1) 4 x ) 3 ÷ ) Paraphrase the rules for Addition, Subtraction, multiplication,

GUIDED PRACTICE for Example – – 2 12 – 4 – 6 A = Use a graphing calculator to find the inverse of the matrix A. Check the result by showing.

Do Now 11/28/11 In your notebook, explain if the equations below are the same line. y – 5 = 3(x + 2) y – 2 = 3(x + 5) y = 3x + 11 y = 3x + 17 No No y –

Remember: Slope is also expressed as rise/run. Slope Intercept Form Use this form when you know the slope and the y- intercept (where the line crosses.

4-5B Write an Equation in Standard Form and in Slope- Intercept Form Algebra 1 Glencoe McGraw-HillLinda Stamper.

Point-Slope Form Linear Equations in Two Variables.

Slope Intercept and Point Slope Formulas. Slope Intercept Formula Y = MX + b  M is the slope of the equation  X is the input of the equation  B is.

Solving Linear Systems Using Substitution There are two methods of solving a system of equations algebraically: Elimination Substitution - usually used.

REVIEW OF 3-1 AND 3-2 A) Solve by graphing y = 2x – 1 y = -3/4x + 10

1. Write the equation in standard form.

Using Slopes and Intercepts

4-5B Write an Equation in Standard Form and in Slope-Intercept Form

Daily Homework Quiz Review 5.3

§ 1.5 Equations of Lines.

Solve the following word problem.

Standard form and Point-slope form of linear equations

Distance Learning Mini Lesson

OBJECTIVE I will use slope-intercept form to write an equation of a line.

4-2 Writing Linear Equations Given the Slope and a Point

Standard Form 4.4.

§ 1.5 Equations of Lines.

Objective The student will be able to:

Break even or intersection

Objective The student will be able to:

4.5 Point-Slope form of a linear equation

Objective The student will be able to:

Honors Algebra II with Trigonometry Mrs. Stacey

Do Now 1) t + 3 = – 2 2) 18 – 4v = 42.

Writing Linear Equations in Standard Form

Writing Linear Equations Given Two Points

Lesson 5.1 – 5.2 Write Linear Equations in Slope-Intercept Form

Write Equations of Lines

Convert Standard to Slope-Intercept

Solving Equations involving Decimal Coefficients

Chapter 2 Section 2 Linear Equations.

Write and graph lines in point-slope form and standard form

Substitute either point and the slope into the slope-intercept form.

Standard Form to Slope-Intercept Form.

Do Now: Find the equation of the straight line that has: slope m = 4

Even better… write it as y = 3x – 6

Objective The student will be able to:

Objective The student will be able to:

3 Chapter Chapter 2 Graphing.

Slope intercept form is:

Writing Equations of Lines

Objective The student will be able to:

Presentation transcript:

Using Equations in Standard and Slope Intercept Form

Standard Form: Ax + By = C Remember: Standard Form: Ax + By = C A (the leading coefficient) must be positive A, B and C must be integers A, B and C will be numbers x and y are the variables Use standard form when you have two independent quantities

9x + 7.5y = 40.50 90x + 75y = 405 90(2) + 75y = 405 and solve Your family is going to see the new Star Wars movie. Adult tickets are $9 and child tickets are $7.50. Your mom, step-dad, and siblings went and they spent $40.50 total on tickets. Let x = adult tix and y = child tix 9x + 7.5y = 40.50 Since we are using standard form, we will multiply through by 10 to clear out decimals. 90x + 75y = 405 How many kids went? 90(2) + 75y = 405 and solve y = 3, 3 kids went

You have $6. 00 to use to buy apples and bananas. If bananas cost $ You have $6.00 to use to buy apples and bananas. If bananas cost $.50 per pound, and apples cost $.30 per pound, write an equation that represents the different amounts of each fruit you can buy Let x = bananas and y = apples .50x + .30y = 6 Since we are using standard form, we will multiply through by 100 to clear out decimals. 50x + 30y = 600 Apples x-intercept (12, 0) I could buy 12 bananas and no apples for $6 y-intercept (0, 20) I could buy 20 apples and no bananas for $6 Or I could buy a few of each as long they total $6 which is represented by all points on the line! Bananas

Slope Intercept Form: y = mx + b Remember: Slope Intercept Form: y = mx + b -Use slope Intercept form when you know (or can calculate) a rate of change -Use if you have an independent and dependent quantity

Real-life application Between 1980 and 1990 the number of vacations taken by Americans increased by about 15,000,000 per year. In 1985 Americans went on 340,000,000 vacation trips. Find an equation that gives the number of vacation trips, y (in millions), in terms of years, t.

A Linear Model for Vacation Travel Solution It is your rate of change. The constant rate is 15 million trips/year, so m= 15 (5, 340) Where 5 represents 1985 340 represents the number of trips in millions Question What is your slope? What is your given point?

So the slope-intercept form of the Now follow the steps and find the equation when m = 15 and the given point is (5, 340) Follow the steps: y = mx + b 340 = 15(5) + b (plug in m, x, and y) 340 = 75 + b (subtract 75 from both sides) 265 = b y= 15x + 265 (plug in the m and b value) So the slope-intercept form of the equation is y=15t+265