Warm up Find the slope of the line that passes through the points (3, 5) and (7, 12). Find the slope of the line that passes through the points (–2, 4)

Slides:

Advertisements

Similar presentations

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–3) CCSS Then/Now New Vocabulary Example 1: Slope and Constant of Variation Example 2: Graph.

Advertisements

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 3) CCSS Then/Now New Vocabulary Key Concept: Slope-Intercept Form Example 1:Write and Graph.

Splash Screen Graphing Equations in Slope-intercept Form Lesson 4-1.

EXAMPLE 2 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.

Splash Screen. Then/Now I CAN write, graph, and solve problems involving direct variation equations. Note Card 3-4A Define Direct Variation and Constant.

Geometry Warm ups What is the slope of the line MN for M(–3, 4) and N(5, –8)? What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?

Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Direct Variation Equations

1.A 2.B 3.C 4.D A.d = 400t; 5 h B.d = 490t; 4 h C.d = 40t; 50 h D.d = 4t; 500 h A baggage train took 3.5 hours to travel 140 miles. Write a direct variation.

Identify, write, and graph an equation of direct variation.

Direct and Inverse Variation

Lesson 12-1 Inverse Variation. Objectives Graph inverse variations Solve problems involving inverse variations.

Drill #61 Find the slope of the line that passes through each pair of points: 1.( 6, -4 ), ( 8, -7 ) 2.( 8, 5 ), ( 8, -1) Determine the value of r so that.

Goal: Use direct variation to solve word problems Eligible Content: A / A

Lesson 2 MI/Vocab direct variation constant of variation family of graphs parent graph Write and graph direct variation equations. Solve problems involving.

Splash Screen Direct Variation Lesson 3-4. Over Lesson 3–3.

3.6 Model Direct Variation

PRE-ALGEBRA. Lesson 8-4 Warm-Up PRE-ALGEBRA What is a “direct variation”? How do you find the constant, k, of a direct variation given a point on its.

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

Algebra 1 Section 4.2 Slope and Direct 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.

1.A 2.B 3.C 4.D 5Min 2-3 Determine the slope of the line that passes through the points (–3, 6) and (2, –6). 11/8 Honors Algebra Warm-up A. B. C.0 D.undefined.

Welcome to Interactive Chalkboard Algebra 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION.

Bell Ringer Learning Target : I can solve an equation for the constant of variation.

10-1 Inverse Variation 10-2 Rational Functions 10-3 Simplifying Rational Expressions 10-4 Multiplying and Dividing Rational Expressions 10-5 Adding and.

Write and graph linear equations in slope-intercept form.

Direct Variation Honors Math – Grade 8. Get Ready for the Lesson It costs $2.25 per ringtone that you download on your cell phone. If you graph the ordered.

Variation and Proportion Direct Proportion. The formula for direct variation can be written as y=kx where k is called the constant of variation.   The.

Lesson: 3.6 Model Direct Variation Essential Question: How do you write and graph direct variation equation? Warm-up: Rewrite the equation so.

Then/Now You found rates of change of linear functions. (Lesson 3–3) Write and graph direct variation equations. Solve problems involving direct variation.

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

Slopes and Direct Variation December 9, Review Slope Slope – Rise Run (-1, -4) and (2, 2)

Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and.

Lesson 5-2 Slope and Direct Variation. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

§2.5 Model Direct Variation CA Standard 2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with.

2.3 Direct Variation. A linear function in the form of y=kx where k is the constant of 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.

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

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 3) CCSS Then/Now New Vocabulary Key Concept: Slope-Intercept Form Example 1:Write and Graph.

Splash Screen. Then/Now You found rates of change of linear functions. Write and graph direct variation equations. Solve problems involving direct variation.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–3) CCSS Then/Now New Vocabulary Example 1: Slope and Constant of Variation Example 2: Graph.

Splash Screen. Concept Example 1 Write and Graph an Equation Write an equation in slope-intercept form of the line with a slope of and a y-intercept.

3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz

X + 2y = 4 xy Solve equation for y. 3x – 2y = -6 xy Solve equation for y.

Direct Variation y = kx. A direct variation is… A linear function Equation can be written in the form; y = mx ; m  0 ory = kx ; k  0 The y-intercept.

5.2 Slope and Direct Variation What you’ll learn: 1.Write and graph direct variation equations. 2.To solve problems involving direct variation.

Warm UpOct. 15  For numbers 1-3, find the slope of the line that passes through each pair of points 1. (-4, -1) and (-3, -3) 2. (-2, 3) and (8, 3) 3.

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%

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

2.5 The Man Who Ran from Marathon to Athens Graphing Direct Proportions WARM UP A baby elephant nurses for the first two years of its life. Shortly after.

Warm Up Find the slope of the line that connects each pair of points. – (5, 7) and (–1, 6) 2. (3, –4) and (–4, 3)

Warm-Up Exercises Lesson x – 2y = –8 2. –9x + 3y = 21 ANSWER y = 2x + 4 Rewrite the equation so y is a function of x. y = 3x + 7.

Direct Variation (3-4) Objective: Write and graph direct variation equations. Solve problems involving direct variation.

LESSON 3–4 Direct Variation.

Algebra 1 Notes Chapter 3.

Variation and Proportion

3-4 Direct Variation Word Problems

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

Direct Variation Equations

Variation and Proportion

Direct Variation Equations

Proportional Relationships and Graphs

5.5 Direct Variation Pg. 326.

Variation and Proportion

Presentation transcript:

Warm up Find the slope of the line that passes through the points (3, 5) and (7, 12). Find the slope of the line that passes through the points (–2, 4) and (5, 4). Find the slope of the line that passes through the points (–3, 6) and (2, –6). In 2005, there were 12,458 fish in Hound’s Tooth Lake. After years of drought, there were only 968 fish in What is the rate of change in the population of fish for 2005–2010?

Find the value of r. (review) A.5 B. C.–5 D.11 Find the value of r so that the line through (r, 4) and (3, –1) has a slope of

3-4 DIRECT VARIATION Objective: Write and graph direct variation equations. Solve problems involving direct variation.

Vocabulary direct variation: an equation in the form y=kx, where k does not equal zero constant of variation / Constant of proportionality: The number k in the equation of the form y=kx

Example 1 A A. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. (x 1, y 1 ) = (0, 0) (x 2, y 2 ) = (1, 2) Answer:The constant of variation is 2. The slope is 2. Slope formula Simplify.

Example 1 B B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Answer: The constant of variation is –4. The slope is –4. (x 1, y 1 ) = (0, 0) (x 2, y 2 ) = (1, –4) Slope formula Simplify.

TOO A. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. A.constant of variation: 4; slope: –4 B.constant of variation: 4; slope: 4 C.constant of variation: –4; slope: –4 D.constant of variation: slope:

TOO B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. A.constant of variation: 3; slope: 3 B.constant of variation: slope: C.constant of variation: 0; slope: 0 D.constant of variation: –3; slope: –3

Step 2Graph (0, 0). Example 2 Step 3From the point (0, 0), move down 3 units and right 2 units. Draw a dot. Step 4Draw a line connecting the points. Step 1 Find the slope. m Answer:

TOO Graph y = 2x. A.B. C.D.

Direct Variation Graphs

Example 3 A A. Suppose y varies directly as x, and y = 9 when x = –3. Write a direct variation equation that relates x and y. Find the value of k. y =kxDirect variation formula 9 =k(–3)Replace y with 9 and x with –3. Divide each side by –3. –3 = kSimplify.

Example 3 A Answer Answer: Therefore, the direct variation equation is y = –3x.

Example 3 B Answer: Therefore, x = –5 when y = 15. B. Use the direct variation equation to find x when y = 15. Simplify. Direct variation equation Replace y with 15. Divide each side by –3.

TOO A.y = 3x B.y = 15x C.y = 5x D.y = 45x A. Suppose y varies directly as x, and y = 15 when x = 5. Write a direct variation equation that relates x and y.

TOO A.–3 B.9 C.–15 D.–5 B. Suppose y varies directly as x, and y = 15 when x = 5. Use the direct variation equation to find x when y = –45.

Example 4 A A. TRAVEL The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. Write a direct variation equation to find the distance driven for any number of hours.

Example 4 A Solve for the rate. Answer: Therefore, the direct variation equation is d = 60t. Simplify. Original equation Divide each side by 5.5.

Example 4 B B.Graph the equation. The graph of d = 60t passes through the origin with a slope of 60. Answer:

Example 4 C Estimate Using Direct Variation C. Estimate how many hours it would take to drive 500 miles. Answer: At this rate, it will take about 8.3 hours to drive 500 miles. Simplify. Replace d with 500. Divide each side by 60. Original equation 8.33 ≈ t 500 = 60t

TOO A. Dustin ran a 26-mile marathon in 3.25 hours. Write a direct variation equation to find the distance run for any number of hours. A.d = h B.d = 8h C.d = 8 D.

TOO B. Dustin ran a 26-mile marathon in 3.25 hours. Graph the equation. A.B. C.D.

TOO C. Estimate how many hours it would take to jog 16 miles. A.1 hour B. C.16 hours D.2 hours

Homework Pg 185 #11-39 odd, 42,43