lesson 2 homework practice slope answers

Slope of a Line Worksheet (pdf) and Answer Key

Students will explore the properties of slope and practice calculating the slope of a line based on two points or from a graph . They will do this through exploratory activities, model problems with visual aids and powerpoints as well as through error analysis.

Example Questions

Draw the picture of a line that has a positive slope .

Draw a line that has a positive slope.

Calculate the slope of a line passing through the points below.

Calculate the slope from the graph below

Visual Aids

Other Details

This is a 4 part worksheet :

• Part I Exploratory activity using online resource
• Part II Model Problems (with an online powerpoint)
• Part III Practice Problems with answers explained online at //mathwarehouse.com/slope5/
• Part IV . Homework. Error analysis as well extra practice problems
• How to Find Slope from Graph

• Interactive Slope : explore the formula of slope by clicking and dragging two points.

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Into Math Grade 8 Module 5 Lesson 2 Answer Key Derive y = mx

We included H MH Into Math Grade 8 Answer Key PDF Module 5 Lesson 2 Derive y = mx to make students experts in learning maths.

HMH Into Math Grade 8 Module 5 Lesson 2 Answer Key Derive y = mx

I Can write the equation of a line given a graph or a table of values.

Spark Your Learning Asiah’s literature class is studying a new book. To complete the assigned reading on time, she has made a schedule. Asiah records her progress in a graph. What can you interpret from the graph?

Turn and Talk How would the graph look differently if she read more pages per day?

Build Understanding

Step It Out

Connect to Vocabulary A linear equation is an equation whose solutions form a straight line on a coordinate plane.

E. Use the graph to predict the number of carvings sold after being in business for 10 months. _______________ F. Use the equation to predict the number of months needed for Don to sell 30 carvings online. _______________

Turn and Talk A line is modeled by the equation y = mx. Explain how the value of m affects the graph of the line. Answer: We have the slope-intercept form of a straight line given by y = mx + b, where m is the slope and b is the y-intercept. If b = 0 then y = mx

Check Understanding

Question 1. The Nguyen family is traveling cross-country, driving 300 miles each day. Let x represent the number of days in the trip and let y represent the total number of miles driven. Write an equation to model their trip. Answer: Given, The Nguyen family is traveling cross-country, driving 300 miles each day. Let x represent the number of days in the trip and let y represent the total number of miles driven. y = 300x Thus the equation to model their trip is y = 300x

Question 2. Write the equation for the line passing through points (0, 0), (4, 5), and (8, 10). Answer: From the coordinate, (0, 0), we can conclude that the y-intercept of the line is 0. (4, 5) and (8, 10) Slope = (y2-y1)/(x2-x1) m = (10 – 5)/(8 – 4) m = 5/4 Thus the equation of the line is y = 5/4x

On Your Own

B. A line is drawn to model the relationship between the number of weeks and the change in price. Is the slope of this line positive or negative? Explain. ________________________ Answer:

C. Write the equation of the line. ________________________ Answer:

Question 4. A line passes through the origin, (5, -15), and (-1, 3). A. Explain how to find the slope of the line. Answer: Let the analytical formula of the straight line be y = kx + b (5, -15), and (-1, 3) Slope = (y2-y1)/(x2-x1) m = (3+15)/(-1-5) m = 18/-6 m = -3

For Problems 5-8. write the equation of the line shown.

For Problems 9-10, sketch the graph of the line represented by the equation. Plot and label three points on each line.

For Problems 11-12, write an equation that models the relationship shown in the table.

For Problems 13-14, write an equation for the line described.

Question 13. a line passing through the origin and (-2.5, 5) _______________________ Answer: The line passing through the origin. y = kx x = -2.5 and y = 5 5 = k . -2.5 k = -5/2.5 k = -2 So, slope is -2

Question 14. a line passing through the origin and (3a, 5g) Answer: The line passing through the origin. y = kx x = 3a and y = 5g 5g = k . 3a k = 3a/5g . x So, the equation is y = 5g/3a . x

I’m in a Learning Mindset!

What challenge did I face when writing an equation that modeled the relationship in the table for Problem 12? ______________________________ ______________________________

Lesson 5.2 More Practice/Homework

Question 1. Sean tutors math students to earn extra money.

A. How much would Sean earn from 4 hours of tutoring? ______________________________ ______________________________ Answer: Sean earn $20 per hour 4 hours = 4 × 20 = $80

B. Write an equation to model Sean’s earnings, y, after x hours. ______________________________ Answer: y = 20x where x represents number of hours and y represents earnings.

Question 2. Attend to Precision An inch is exactly 2.54 centimeters. Write an equation to convert the number of inches x to the corresponding length in centimeters. Answer: Given, An inch is exactly 2.54 centimeters. 1 cm = 0.39 inch y = 2.54x

Question 3. Write an equation of the line passing through the points (-5, -25), (0, 0), and (3, 15). Answer: (-5, -25), (0, 0), and (3, 15) -25 = m(-5) + b ⇒ 5m – b = 25 0 = m(0) + b ⇒ b = 0 5m – 0 = 25 5m = 25 m = 5 5m – b = 25 5(5) – b = 25 25 – b = 25 25 – 25 = b b = 0 y = mx + b y = 5x + 0 y = 5x

Question 4. Math on the Spot The graph shows the distance Caleb runs over time. A. Identify four points on the line. _______________________ Answer: Four points on the line are (0, 0), (8, 1), (16, 2) and (24, 3)

B. Determine the slope of the line. _______________________ Answer: 8 min = 1 mile 1 min = 1/8 mile y = kx k = 1/8 So, the slope of the line is 1/8.

C. Write an equation of the line. _______________________ Answer: If y = kx + b k = 1/8 and b = 0 Thus the equation of the line is y = 1/8 x

Question 7. What is the equation of the line passing through the points (-2, 5), (0, 0), and (4, -10)? A. y = –\(\frac{5}{2}\)x B. y = –\(\frac{2}{5}\)x C. y = \(\frac{2}{5}\)x D. y = \(\frac{5}{2}\)x Answer: Given points (-2, 5), (0, 0), and (4, -10) -2m + b = 5 m(0) + b = 0 b = 0 5 = -2m m = -5/2 y = -5/2x Thus option A is the correct answer.

Spiral Review

Question 11. Triangle ABC has vertices (1, 4), (5, 6), and (3, 10). It is reflected across the y-axis, forming Triangle A’B’C’. What are the vertices of the new triangle? Answer: Given, Triangle ABC has vertices (1, 4), (5, 6), and (3, 10). It is reflected across the y-axis, forming Triangle A’B’C’. A'(-1, 4), B'(-5, 6) and C'(-3, 10)

Question 12. Quadrilateral ABCD is dilated by a scale factor of 2, with the center of dilation at the origin. The vertices of ABCD are A(0, 0), 8(5, 0), C(5, 3), and 0(0, 3). What are the coordinates of the image of Vertex C under the dilation? Answer:

Question 13. Solve the equation 3x – 2(x + 1) = 2x – 7. Answer: 3x – 2(x + 1) = 2x – 7 3x – 2x – 2 = 2x – 7 x – 2x = 2 – 7 -x = -5 x = 5

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