Homework (Tuesday, 11/17) Lesson 3.08 packet variation-definition/constant-of-variation-definition.

Slides:

Advertisements

Similar presentations

Entry Task – SHOW WORK

Advertisements

What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

Direct Variation.

Direct Variation Objective: Students will be able to identify, write and graph direct variation equation.

3.4 – Slope & Direct Variation. Direct Variation:

The general equation for DIRECT VARIATION is k is called the constant of variation. We will do an example together.

Slope. Direct Variation What you’ll learn To write and graph an equation of a direct variation. Direct variation and Constant of variation for a direct.

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

Direct and Inverse Variations Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases.

Direct and Inverse Variation

Warm up Determine the asymptotes for: 1. x=-2, x=0, y=1.

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

What day is it? Lesson: Direct Variation - Constant k??

Direct and Inverse Variations Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases.

Algebra 1 Section 4.2 Slope and Direct Variation.

Direct and Inverse Variation. Direct Variation Y varies directly to x, when x and y are related by the equation: y=kx. Here k is the constant of variation.

2.4 Writing Equations of Lines. We’ve learned to graph given an equation. Now we’ll learn to write the equation given the graph There are three ways.

Direct and Inverse.

2.4 Writing Equations of Lines p. 91. Learning Target I can write equations of a line.

Variation Functions Essential Questions

Inverse Variation 1) In an inverse variation, the values of the two x and y change in an opposite manner - as one value increases, the other decreases.

Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?

Section 1-3: Graphing Data

Bellringer Put your name at the top of the paper 1. Is the set {(2,0), (-1, 9), (4,-2), (3,0), (1,9)} a function? 2. Find the slope of the line that passes.

Section 4.5 Direct Variation. What happens to Y as X goes up by 1?

DIRECT VARIATION GOAL: WRITE AND GRAPH DIRECT VARIATION EQUATIONS Section 2-6:

Section Direct and Inverse Variation. Lesson Objective: Students will: Formally define and apply inverse and direct variation.

Chapter 12 Rational Expressions and Functions 12 – 1 Inverse Variation If you are looking at the relationship between two things and one increases as the.

k is called the constant of variation or constant of proportionality.

Slope and Direct Variation Mr Smith. By the end of this…  You should know what direct variation is, why it is important, and how you could use it. 

Direct Variation Chapter 5 Section 2. Objective  Students will write and graph an equation of a direct variation.

8-1/2-2 DIRECT AND INVERSE VARIATION. Direct Variation Equation: y = kx Solve for constant “k” k = y/x As x increases, y increases As x decreases, y decreases.

5.5 Direct Variation Pg Math Pacing Slope Review.

What do you guess?. # of hours you studyGrade in Math test 0 hour55% 1 hour65% 2 hours75% 3 hours95%

Warm Up Write down objective and homework in agenda Lay out homework (Graphical stories wkst) Homework (WB 5-5)

Lesson 5.2 Direct Variation Direct variation y = kx Where k is the constant of variation.

Inverse Variation Lesson 11-1 SOL A.8. Inverse Variation.

Direct, Inverse & Joint Variation Section 2.5. Direct Variation 2 variables X & Y show direct variation provided y = kx & k ≠ 0. The constant k is called.

Direct Variation If two quantities vary directly, their relationship can be described as: y = kx where x and y are the two quantities and k is the constant.

Direct and Inverse Variations

Direct and Inverse.

9.1 Inverse & Joint Variation

Mathematical Relationships

Direct and Inverse.

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Direct Variation Lesson 2-3.

2.2 Direct Variation P68-70.

Inverse & Joint Variation

Lesson 5-5 Direct Variation

Warm-up b) a) Solve the following equation.

5-2 Direct Variation What is Direct Variation?

Inverse Variation Chapter 8 Section 8.10.

Direct and Inverse.

4.2 Slope & Direct Variation

Direct and Inverse Variations

Direct and Inverse Variations

Direct and Inverse Variations

Lesson 5-2 Direct Variation

Direct and Inverse.

Direct & Inverse Variation

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

Direct Variation Equations

Direct and Inverse.

Direct and Inverse.

Direct Variation Equations

Mathematical Relationships

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

Direct Inverse and VARIATION.

5.5 Direct Variation Pg. 326.

Presentation transcript:

Homework (Tuesday, 11/17) Lesson 3.08 packet variation-definition/constant-of-variation-definition

Per 3: Extra Credit for no missing assignments Trevor, Jonathan, Angie, Briana, Paul, Teo, Arenui, Maya, Karen, Arman, Pejhon, Naylie, Victoria, Jamie

Per 4: Extra Credit for no missing assignments Hamzeh, Francisco, Nathan, Arthur, Jose, Monaghan, Charli, Ashley, Alejandro, Daisy, Ava, Preston, Alexis, Ana, Katelyn, Sebastian, Oliver, Andrea

Per 5: Extra Credit for no missing assignments Azam, Sean B, Luis, Carly, Caroline G, Peyton, Karina, Kimberly, Nikki, Jennifer P, Abby, Sofia, Nan, Annabelle, Morgan, Jacob

Lesson Direct and Inverse Variations

Direct Variation a relationship where as x increases and y increases or x decreases and y decrease at a CONSTANT RATE. Formula: y = kx, where k cannot be zero and k is called constant variation

What does the graph y=kx look like? A straight line with a y-intercept of 0. y=3x

Looking at the graph, what is the slope of the line? Answer: 3 Looking at the equation, what is the constant of variation? Answer: 3 The constant of variation and the slope are the same!!!!

Direct Variation Direct variation uses the following formula:

Direct Variation Example 1: if y varies directly as x and y = 10 as x = 2.4, find x when y =15.

Direct Variation If y varies directly as x and y = 10 find x when y =15. y = 10, x = 2.4 make these y 1 and x 1 y = 15, and x = ? make these y 2 and x 2

Direct Variation if y varies directly as x and y = 10 as x = 2.4, find x when y =15

Direct Variation How do we solve this? Cross multiply and set equal.

Direct Variation We get: 10x = 36 Solve for x by diving both sides by 10. We get x = 3.6

Direct Variation Example 2: If y varies directly with x and y = 12 when x = 2, find y when x = 8.

Direct Variation If y varies directly with x and y = 12 when x = 2, find y when x = 8.

Direct Variation Cross multiply: 96 = 2y Solve for y. 48 = y.

Inverse Variation

In Inverse variation we will Multiply them. x 1 y 1 = x 2 y 2

What does the graph of xy=k look like? Let k=5 and graph.

This is a graph of a hyperbola. Notice: That in the graph, as the x values increase the y values decrease. Also, as the x values decrease the y values increase.

Inverse Variation Example 3: If y varies inversely with x and y = 12 when x = 2, find y when x = 8. x 1 y 1 = x 2 y 2 2(12) = 8y 24 = 8y y = 3

Inverse Variation Example 4: If y varies inversely as x and x = 18 when y = 6, find y when x = 8. 18(6) = 8y 108 = 8y y = 13.5