Equations of proportional relationships

Slides:

Advertisements

Similar presentations

Identifying and Representing Proportional Relationships

Advertisements

Constant of Proportionality

Unit 7: Direct Proportion Direct Proportion Notes Ms. Shivertaker Lovinggood MS.

3.4 – Slope & Direct Variation. Direct Variation:

Direct and Inverse Variation

Constant of Proportionality

Direct Variation What is it and how do I know when I see it?

Direct Variation What is it and how do I know when I see it?

Direct & Indirect Relationships in

Warm-Up 2 1.Solve for y: 2x + y = 6 2.Solve for y: 2x + 3y = 0.

Representing proportional relationships with equations.

Warm Up Exercise  Solve each equation for the given variable: (1) V = LWH solve for W (2) A = ½ BH solve for H (3) ax + by = 0 solve for y.

4.5 Direct Variation What is it and how do I know when I see it?

I can write and graph an equation of a direct variation by identifying the constant of variation.

5-2 Direct Variation A direct variation is a relationship that can be represented by a function in the form y = kx, where k ≠ 0. The constant of variation.

Representing Proportional Relationships with Equations.

Unit 3, Lesson 6 Constant of Proportionality and Writing Direct Variation Equations.

ALGEBRA READINESS LESSON 8-6 Warm Up Lesson 8-6 Warm-Up.

Variation Functions Essential Questions

Direct Variation Section 1.9.

U SING D IRECT AND I NVERSE V ARIATION D IRECT V ARIATION The variables x and y vary directly if, for a constant k, k  0. y = kx, Objective Lesson 11.3.

Direct variation.

Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.

I can write and graph an equation of a direct variation.

Constant of Proportionality. A direct variation is represented by a ratio or equation : or k ≠ 0 Direct Variation – constant ratio EX1) Determine if the.

LESSON How can you use tables, graphs, and equations to represent proportional situations? Representing Proportional Relationships.

Constant of Proportionality. A direct variation is represented by a ratio or equation : or k ≠ 0 Direct Variation – constant ratio EX1) Determine if the.

Using y = 8x, what is the value of x if y = 72? Complete the table of values for 4x = y X0123 Y.

Writing a direct variation equation. write a direct variation problem when y = 20 and x = 10 y = kx 20 = k·10 k = 2 y = 2x.

NOTES 2.3 & 9.1 Direct and Inverse Variation. Direct Variation A function in the form y = kx, where k is not 0 Constant of variation (k) is the coefficient.

Direct Variation 88 Warm Up Use the point-slope form of each equation to identify a point the line passes through and the slope of the line. 1. y – 3 =

Proportional Relationships and Graphs

Proportional Relationships

DIRECT VARIATIONS.

Constant of Proportionality

Direct Variation.

Chapter 8: Rational & Radical Functions

Algebra 1 Section 4.5 Solve direct variation problems

Constant of Proportionality

2.2 Direct Variation P68-70.

Warm Up Solve each proportion. = = 1. b = y = 8 = = m = 52

5-2 Direct Variation What is Direct Variation?

Direct Variation Chapter 8 Section 8.9.

2.3: Direct Variation Objective: Determine if a function is a direct variation function.

5-2 Direct Variation.

2.3: Direct Variation Objective: Determine if a function is a direct variation function.

Algebra November 12, Direct Variation Objective:

What is it and how do I know when I see it?

Recall that a proportional relationship is a relationship between two quantities in which the ratio of one quantity to the.

Direct Variation Direct Variation: y y

Warm Up – August 14, 2017 Solve for y. 3 + y = 2x 6x = 3y

Direct Proportion also known as Direct Variation

Old Thoughts…… Proportional relationships have a constant ratio, or unit rate. The graph of a proportional relationship is a straight line that passes.

Linear Relationships Graphs that have straight lines

Constant of Proportionality Pg. 40 & 41 RS

What is it and how do I know when I see it?

Proportional Relationships and Graphs

Direct Variation.

Linear proportional relationship Linear non-proportional relationship

Homework: Maintenance Sheet 15 via study island due Friday

What is it and how do I know when I see it?

Proportional or Non-proportional?

What is it and how do I know when I see it?

What is it and how do I know when I see it?

Direct Variation.

What is it and how do I know when I see it?

What is it and how do I know when I see it?

What is it and how do I know when I see it?

What is it and how do I know when I see it?

Presentation transcript:

Equations of proportional relationships

Equations of Proportional Relationships What we’ve learned….. Proportional relationships have a constant ratio, or unit rate. The constant ratio, or unit rate, can also be called the constant of proportionality. The graph of a proportional relationship is a straight line that passes through the origin.

Equations of Proportional Relationships New vocabulary….. A proportional relationship can be called a direct variation. Proportions can be represented by the equation y = kx where k is the constant of proportionality.

Writing an equation from the graph of a proportional relationship Ex. 1) The number of students that can go on a trip is proportional to the number of chaperones that are available. A) Find the constant of proportionality k, or the unit rate, of this relationship. (4, 24) (3, 18) (2, 12) (1, 6) B) Write an equation to represent this relationship. y = kx No. of students No. of chaperones y = 6x

Writing an equation from a table of values Ex. 2) In Mrs. McCarthy’s new car, the number of miles driven is proportional to the gallons of gas used. B) Write an equation to represent this relationship. A) Find the constant of proportionality k, or the unit rate, of this relationship. y = kx Gallons of gas used No. of miles y = 30x

Writing an equation from a verbal statement Ex. 3) If y varies directly with x, write the equation for this relationship if y = 6 when x = 2. A) Find the constant of proportionality k, or the unit rate, of this relationship. B) Write an equation to represent this relationship. y = kx y = 3x y = 3x C) What is the value of y when x=7? y = 3(7) y = 21 when x = 7

Writing an equation from a verbal statement Ex. 4) It costs $5 to send 6 packages through a certain shipping company. Consider the number of packages per dollar. A) Find the constant of proportionality k, or the unit rate, for this situation. B) Write an equation to represent this relationship. Number of packages y = k(dollars x) y = 1.2x