4.1 & Linear Equations in Slope-Intercept Form

Transcription

1 4.1 & Linear Equations in Slope-Intercept Form Slope-Intercept Form: y = mx + b Ex 1: Write the equation of a line with a slope of -2 and a y-intercept of 5. Ex 2:Write an equation of the line shown in the graph. Ex 3: Write an equation of the line. shown in the graph. You can write an equation of a line given the following pieces of information: A slope and a y-intercept A slope and a point Two points Ex 4: What is the equation of a line with a slope of 1/4 and an x-intercept 5? (Hint: What information are you given?) What equation in slope-intercept form represents the line that passes through the points: Ex 5: (1, 6) and (3, -4) Ex 6: (-3, 1) and (5, 5) Ex 7: (2, 1) and (5, -8)

2 4.5 Write Equations of Parallel & Perpendicular Lines Parallel Lines- never intersect and have the SAME slope ( ) Perpendicular Lines- intersect at a right angle and their slopes are opposite reciprocals ( ) **If you are told to write an equation or to another line, the only piece of information that you need is the slope. Ex 8: Write the equation of a line that passes through (-2, 1) and is parallel to y = (2/3)x - 2. Ex 9: Write the equation of a line that passes through (3, 7) and is perpendicular to y = (-3/4)x + 2. Ex 10: Quadrilateral ABCD has vertices A(-1, 2), B(2, 3), C(3, 0) and D(0, -1). Write the equation of all 4 lines.

3 Section 4.3 Point-Slope Form Point-Slope Form: y y 1 = m(x x 1 ) m -> slope, (x 1, y 1 ) -> fixed point Write in point-slope form. Ex 1: (-6, 8) m = 3 Ex 2: (-3, 6) & (1, -2) Write in point-slope form, then slope-intercept form. Ex 3: (2, -1) m = -1 Ex 4: (-3, 6) m = -5 Ex 5: Write an equation of this line in Ex 6: What is the graph of the point-slope form. equation y + 1 = 2/3(x - 2)? Ex 7: The table shows the altitude of a hot-air balloon during its linear descent. Write an equation in point-slope form to represent the given scenario. Rewrite it in slope-intercept form. What do the slope and y-intercept represent?

4 4.4 Write Equations in Standard Form Standard Form: Ax + By = C A, B and C are integers and A and B are not both zero. Helpful Hints: - y-intercept: x = 0 - x-intercept: y = 0 -Standard form allows you to find the intercepts quickly Ex 1: What are the x and y-intercepts of the graph of 3x + 4y = 24. Ex 2: Graph x - 2y = -2. Write in standard form using integers. Ex 3: 2 y x 3 Ex 4: (-4, 3) m = -2 5 Ex 5: (1, -4) m = 0 Ex 6: (1, 4) & (5, 7) Practice on your own (Write in Standard Form): Ex 7: y = -5/6x + 4 Ex 8: (5, -2) & m = ½ Ex 9: (-4, 1) & (2, -5) Ex 10: (8, -7) & m = Undefined

5 Chapter 4 Word Problems Key to success -> identify the information given to you. Were you given: A rate of change and a starting point/initial value? A rate of change and a point? Two points? Ex 1: California had a population of about million. During the next 15 years, the state s population was expected to increase by an average of about 0.31 million people per year. Write an equation to model the population of California between 1990 and How many people were expected to live in California in 2005? Ex 2: Between 1985 & 1995, the number of vacation trips in the United States taken by US residents increased by about 27 million per year. In 1993, US residents went on 740 million vacation trips within the US. Write a linear equation to represent the number of trips taken since How many trips would you estimate were taken in 2005? Ex 3: While working at an archaeological dig, you find an upper leg bone (femur) that belonged to an adult human male. The bone is 43 cm long. In humans, femur length is linearly related to height. To estimate the height of the person, you measure the femur and height of two complete male adult skeletons found at the same excavation. The measurements are as follows: Person 1: 40 cm femur, 162 cm height Person 2: 45 cm femur, 173 cm height. Write an equation to model this information, then use it to determine the height of a male with a femur length of 43 cm.

6 4.6 Fit a Line to Data (Scatterplots) Vocabulary: Scatter plot: A graph used to determine whether there is a relationship between paired data. Correlation: The relationship between two data sets. Line of best fit: A model used to represent the trend in data showing a positive or negative correlation. Using a Line of Best Fit to Model Data Step 1: make a scatter plot of the data Step 2: decide whether the data can be modeled by a line (positive or negative) Step 3: Draw a line that appears to fit the data closely. There should be approximately as many points above the line as below it. Step 4: Write an equation using two points on the line. The points do not have to represent actual data pairs, but they must lie on the line of fit. Ex 1: Game Attendance: The table shows the average attendance at a school s varsity basketball games for various years. Write an equation that models the average attendance at varsity basketball games as a function of the number of years since 2000.