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

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

Lesson 7 MI/Vocab parallel lines perpendicular lines Write an equation of the line that passes through a given point, parallel to a given line. Write an.

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.

Example 1 Write an Equation Given the Slope and a Point Write an equation of a line that passes through (2, –3) with slope Step 1.

Splash Screen Chapter 9 Lesson A 2.B 3.C 4.D Solve the inequality –2x ≤ 5. Then check your solution. (over Chapter 8) A. B. C. D.

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

Over Lesson 8–7 A.A B.B C.C D.D 5-Minute Check 1 Find the slope and y-intercept for the graph of y = x + 5. Find the slope and y-intercept for.

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)

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.

3.4 – Slope & Direct Variation. Direct Variation:

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

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.

Write the equation of a line in point-slope form.

Over Lesson 8–9 A.A B.B C.C D.D 5-Minute Check 1 Which is an equation for the line of best fit for the scatter plot where x is the years since 1998 and.

Then/Now You recognized arithmetic sequences and related them to linear functions. (Lesson 3–5) Write an equation for a proportional relationship. Write.

Use proportions to solve problems.

Then/Now You found rates of change and slopes. (Lesson 3–3) Write and graph linear equations in slope-intercept from. Model real-world data with equations.

Lesson 7 MI/Vocab scale drawing scale model scale Solve problems involving scale drawings.

Lesson 1 MI/Vocab rate of change slope Use rate of change to solve problems. Find the slope of a line.

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

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

3.6 Model Direct Variation

Lesson 3 Menu Five-Minute Check (over Lesson 10-2) Main Ideas and Vocabulary Targeted TEKS Example 1: Variable in Radical Example 2: Radical Equation with.

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.

Algebra 1 Section 4.2 Slope and Direct 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.

Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation.

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.

Then/Now You graphed ordered pairs in the coordinate plane. (Lesson 1–6) Use rate of change to solve problems. Find the slope of a line.

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

Lesson 6 Menu 1.Determine whether the dilation is an enlargement, reduction, or congruence transformation for a scale factor of r= 2/3. 2.Determine whether.

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 5 MI/Vocab slope-intercept form y-intercept Graph linear equations using the slope and y-intercept.

Write equations of lines in point-slope form.

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.

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

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.

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

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.

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.

Welcome to Interactive Chalkboard

LESSON 3–4 Direct Variation.

Direct Variation Lesson 2-3.

Algebra 1 Notes Chapter 3.

Lesson 5-2 Direct Variation

3-4 Direct Variation Word Problems

Direct Variation Equations

Direct Variation Equations

5.5 Direct Variation Pg. 326.

Chapter 4-7 Parallel Lines

Presentation transcript:

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

Lesson 2 Ex1 Slope and Constant of Variation 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.

Lesson 2 Ex1 Slope and Constant of Variation 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.

A.A B.B C.C D.D Lesson 2 CYP1 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:

A.A B.B C.C D.D Lesson 2 CYP1 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

Lesson 2 Ex2 Graph a Direct Variation A.Graph y = x. Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot. Step 4Draw a line connecting the points.

Lesson 2 Ex2 Graph a Direct Variation Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move down 3 units and right 2 units. Draw a dot. Step 4Draw a line connecting the points. B.

Lesson 2 CYP2 1.A 2.B 3.C 4.D A. Graph y = 2x. A.B. C.D.

Lesson 2 CYP2 1.A 2.B 3.C 4.D B. A.B. C.D.

Lesson 2 CS 1

Lesson 2 Ex3 Write and Solve a Direct Variation Equation 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. Direct variation formula Replace y with 9 and x with –3. Divide each side by –3.

Lesson 2 Ex3 Write and Solve a Direct Variation Equation –3 = kSimplify. Answer: Therefore, the direct variation equation is y = –3x.

Lesson 2 Ex3 Write and Solve a Direct Variation Equation 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.

1.A 2.B 3.C 4.D Lesson 2 CYP3 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.

1.A 2.B 3.C 4.D Lesson 2 CYP3 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.

Lesson 2 Ex4 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. Direct Variation Words Distance equals rate times time. Let r = rate. Variable 330 mi =r × 5.5h Equation

Lesson 2 Ex4 Solve for the rate. Answer: Therefore, the direct variation equation is d = 60t. Direct Variation Simplify. Original equation Divide each side by 5.5.

Lesson 2 Ex4 B.Graph the equation. The graph of d = 60t passes through the origin with a slope of 60. Answer: Direct Variation

Lesson 2 Ex4 C. Estimate how many hours it would take to drive 600 miles. Answer: At this rate, it will take 10 hours to drive 600 miles. Direct Variation Simplify. Replace d with 600. Divide each side by 60. Original equation

A.A B.B C.C D.D Lesson 2 CYP4 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.

A.A B.B C.C D.D Lesson 2 CYP4 B. Dustin ran a 26-mile marathon in 3.25 hours. Graph the equation. A.B. C.D.

A.A B.B C.C D.D Lesson 2 CYP4 C. Estimate how many hours it would take to jog 16 miles. A.1 hour B. C.16 hours D.2 hours