Algebra 1 Keystone Remediation Packet. Module 2 Anchor 2. Name

Transcription

1 Algebra 1 Keystone Remediation Packet Module 2 Anchor 2 A Identify, describe, and/or use constant rate of change. A Apply the concept of linear rate of change to solve problems. A Write or identify a linear equation when given a graph, two points, or a slope and one point. Linear equation may be in point-slope, standard, or slope intercept forms. A Determine the slope and/or y-intercept represented by a linear equation or a graph. A Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot. Analyze and/or interpret data on a scatter plot. Name

2 Slope is the measure of the steepness of the line. Slope is can be described as a constant rate. Slope Slope is a ratio that compares the change in vertical distance to the change in horizontal distance. If you are given two points (D E, G E ) IJK (D L, G L ), you can calculate the slope with this formula. M = G L G E D L D E There are four types of slope, based upon the value of M. Example: Calculate the slope of the line that passes through the points (2,1) (5,2) Represent this line on the graph below.

3 Linear Equations A linear equation is an equation that when graphed is shaped like a line. The line may be horizontal, vertical, or diagonal. Slope-intercept form G = MD + Z, where M = [\]^_, Z = G `Ja_bc_^a You can easily identify the slope of this line (M). You can display the graph in your graphing calculator. Point-slope form G G E = M(D D E ), where M = [\]^_ You can easily identify the slope of this line (M). Point slope form is used when you are given a point (D E, G E ) and a slope. Standard form ed + fg = g, where e, f, g are constants You can easily identify the x and y intercepts. You can convert this to slope intercept form. You may be asked to write an equation of the line that passes through the points (D E, G E ) IJK (D L, G L ). There are two ways to do this. Method 1: First calculate the slope. Then use one of the points to calculate the y-intercept. Method 2: First calculate the slope. Then use one of the points as (D E, G E ), and write the line in pointslope form.

4 Graphing Practice Graph G = D Slope is E E Graph G = D Slope is ke E Graph G = 5 Graph D = 5 *Graphs with only the y variable *Graphs with only the x variable are horizontal lines. (Zero slope) are vertical lines. (Undefined slope)

5 Keystone Practice Problems A Identify, describe, and/or use constant rate of change. A Apply the concept of linear rate of change to solve problems. 1) A ball rolls down a ramp with a slope of L. At one point the ball is 10 feet high, and at o another point the ball is 4 feet high, as shown in the diagram below. What is the horizontal distance (x) the ball travelled as it rolled down the ramp from 10 feet high to 4 feet high? a. 6 b. 9 c. 14 d. 15 2) A submarine rose to the surface of the ocean at a slope of E, as shown in the diagram below. p What is the horizontal distance that the submarine traveled between when the submarine was 75 feet off of the sea floor and when the submarine was 125 feet above the see floor? Linear Equations

6 3) An airplane climbs at a slope of u at takeoff. At point A, the plane is 200 feet above the p ground. The plane traveled 500 feet horizontally, as shown in the diagram below. What is the altitude (vertical distance) of the plane at point B? 4) A jet climbs at a slope of p EL at take off. At point A, the jet is 50 feet above the ground and at point B the jet is 100 feet above the ground. What is the horizontal distance that the jet traveled between point A and point B? a) 41.6 feet b) 50 feet c) 100 feet d) 120 feet

7 Keystone Practice Problems A Write or identify a linear equation when given a graph, two points, or a slope and one point. Linear equation may be in point-slope, standard, or slope intercept forms. A Determine the slope and/or y-intercept represented by a linear equation or a graph. 1) A line is shown in the graph below. What is the slope of the line? a) E u b) -2 c) E L d) -4 2) A function of x is graphed on the coordinate plane below. What is the slope of the graph? a. 0 E b. p c. 5 d. undefined 3) The equation of a line is shown below. What is the slope of the line? a) u o b) 4 c) u o d) -4 4D 3G = 12

8 4) What is the slope of the line 3D + 2G = 10? a) M = 2 b) M = o L c) M = 3 d) M = L o 5) A function of x is graphed on the coordinate plane. Which equation describes the function? a. G = L o D 4 b. G = L o D + 6 c. G = o L D 4 d. G = 4D + L o 6) The table below represents a function. Which linear equation describes the relationship between x and y? a. G = 2D + 2 b. G = D + 4 c. G = D + 2 d. G = 2D + 4 7) A graph of a linear equation is shown below. Which equation describes the graph? a. G = 0.5D 1.5 b. G = 0.5D + 3 c. G = 2D 1.5 d. G = 2D + 3

9 8) The ordered pairs shown below are on the same line. 6, 4 (12, 6). Which equation describes the relationship between the x coordinates and the y coordinates in the ordered pairs? a. G = 3D 14 b. G = 3D 6 c. G = { D + 10 d. G = { D + 2 9) The graph on the coordinate grid below shows the number of gallons of gas (g) remaining in the tank of Edward s truck based on the number of miles (m) he has driven it. Which equation describes the graph? a. } = 20 1/10M b. } = /10M c. } = M d. } = M 10)

10 Constructed Response (Show your work) 11) There was a layer of snow on Joe s driveway when it began to snow. As the snow fell, Joe measured the depth in centimeters of snow on his driveway. After 5 minutes, he measured 2 centimeters of snow on his driveway. After 25 minutes, the snow was 4 centimeters deep. The snow continued to fall at the same constant rate. Joe graphed a line to represent the snow fall. A. Find the rate of change (slope) and interpret the slope in context. B. Find the y-intercept. What does this point represent in context? C. Write the equation of the line. D. In how many minutes, will the depth of snow be 8 centimeters?

11 Constructed Response (Show your work) 12) To save space in the cupboard, a person stacks salad bowls one inside of the other. The height of 1 bowl is 2 inches. The height of a stack of five bowls is 4 inches. A. Write the ordered pairs (x, y). What does the x variable represent? What does the y variable represent? B. Find the rate of change (slope) and interpret the slope in context. C. Write the equation of the line. Assume the number of bowls is always positive. D. What would the height be for a stack of 15 bowls?

12

13

14

15

16 Scatterplots and Lines of Best Fit A Draw, find, and/or write an equation for a line of best fit for a scatterplot A scatterplot is a type of graph that shows the relationship between two sets of numerical data. They are graphed as ordered pairs on a coordinate plane. There are three types of relationships between data sets, known as correlations. The correlation describes the trends in the data. You can write a line of best fit for a scatterplot that has a positive or negative correlation.

17 Keystone Practice Problems A Draw, find, and/or write an equation for a line of best fit for a scatterplot Analyze and/or interpret data on a scatter plot. 1) The scatter plot below shows the arm spans and heights of 20 people in Dorian s class. Based on the line of best fit, which is most likely the height of a person with an arm span of 200 cm? a) 188 cm b) 192 cm c) 197 cm d) 205 cm 2) The scatter plot below shows the relationship between the time, in minutes, and the distance, in miles, that Julie walked on several occasions. Based on the line of best fit, which is most likely the number of miles Julie would walk in 105 minutes? a) 4 b) 5 c) 6 d) 7

18 Keystone Practice Problems 1) The scatter plot below shows the cost y, of ground shipping packages from Harrisburg PA to Minneapolis MN based on the package weight x. Which equation describes the line of best fit for the scatter plot? a) G = 0.37D b) G = 0.37D c) G = 0.68D d) G = 0.68D ) The scatterplot below shows the cost (y) in dollars, of orange trees based on their ages (x) in years. Based on the scatterplot, which equation represents the line of best fit for the cost of the orange trees?

19

20