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Math Models with Applications HS Mathematics Unit: 05 Lesson: 02 Slope, Intercepts, and Equations of Lines (pp. 1 of 5) One specific type of relation is the ____________________. The linear parent function is ________. Important parts of a linear function are the _________________ and ________________. Slope – ________________________ Methods to determine slope rise . From a graph, count run From a table find the average From an equation y 'y change in y or . 'x change in x mx b , the slope is the m value. Intercepts – ____________________________________________ y-intercept (0, y) From a graph determine where the line crosses the y-axis. Graph points and extend the line if necessary. From an equation in the form y mx b , the y-intercept is the b value. From other equations plug in 0 for x and solve for the y value. x-intercept (x, 0) From a graph determine where the line crosses the x-axis. Graph points and extend the line if necessary. From an equation plug in 0 for y and solve for the x value. Equations of lines x _____________________: ax + by = c (No fractions and x is positive value) x ____________________________: y mx b To determine the equation of the line: x With slope and intercept plug into y mx b . x With a slope and point use the slope to determine a second point, and calculate a line of regression. x With two points calculate a line of regression. x With a table of values calculate a line of regression. When using two points to calculate the line of regression, the calculator will give you an r value of +1 or -1. What does this indicate? © 2009, TESCCC 08/01/09 page 22 of 50 Math Models with Applications HS Mathematics Unit: 05 Lesson: 02 Slope, Intercepts, and Equations of Lines (pp. 2 of 5) Special lines x x = # Vertical line, undefined slope x y = # Horizontal line, zero slope x Parallel lines have equal slope. x Perpendicular lines have negative reciprocal slope. Sample Problems: 1. 2. a. Set up a table of values for at least four points. b. Find the slope. c. Determine the equation of the line. d. Identify the x- and y-intercepts. © 2009, TESCCC a. Set up a table of values for at least four points. b. Find the slope. c. Determine the equation of the line. d. Identify the x- and y-intercepts. 08/01/09 page 23 of 50 Math Models with Applications HS Mathematics Unit: 05 Lesson: 02 Slope, Intercepts, and Equations of Lines (pp. 3 of 5) 3. x -1 1 3 5 y 10 4 -2 -8 a. Find the slope. b. Determine the equation of the line. c. Graph the function. d. Identify the x- and yintercept. 5. y a. b. c. d. 2 x4 3 Set up a table of values. (at least four points) Graph the function. Find the slope. Identify the x- and yintercepts. © 2009, TESCCC 4. x -3 -1 0 2 y -7 -1 2 8 a. Find the slope. b. Determine the equation of the line. c. Graph the function. d. Identify the x- and yintercept. 6. y = 2x - 7 a. Set up a table of values. (at least four points) b. Graph the function. c. Find the slope. d. Identify the x- and yintercepts. 08/01/09 page 24 of 50 Math Models with Applications HS Mathematics Unit: 05 Lesson: 02 Slope, Intercepts, and Equations of Lines (pp. 4 of 5) Practice Problems 1. For the function graphed above: a. Set up a table of values. (at least four points) b. Find the slope. c. Determine the equation of the line. d. Identify the x- and y-intercepts. 2. For the table below: a. Find the slope. b. Determine the equation of the line. c. Graph the function. d. Identify the x- and y-intercepts. x -6 -3 3 9 © 2009, TESCCC y 3 4 6 8 08/01/09 page 25 of 50 Math Models with Applications HS Mathematics Unit: 05 Lesson: 02 Slope, Intercepts, and Equations of Lines (pp. 5 of 5) 3 x 5 2 Set up a table of values. (at least four points) Graph the function. Find the slope. Identify the x- and y-intercepts. 3. For the equation y a. b. c. d. Given information, find the equation of the line in y-intercept form. 4. Contains point (-1, 2) and is parallel to 4x – 2y = -3 5. Contains point (5, -3) and is perpendicular to y = 5x - 4 6. Contains (-4, 3) and is perpendicular to y = 2 7. Contains (8, -1) and is parallel to y = 1 8. Sue Ellen works at JoAnn’s Dress Shop. She is paid a salary of $280 dollars a week plus 20% commission on her sales. Create a data table and determine a rule to represent the amount Sue Ellen is paid as a relation of the amount of sales she makes in the week. a. What is the rate of change? What does it represent in the problem situation? b. What is the y-intercept? What does it represent in the problem situation? c. What is the x-intercept? What does it represent in the problem situation? d. If Sue Ellen sold $500 in merchandise during the week, what would be her total pay? e. On Sue Ellen’s biggest selling week of the year, her total pay was $760. How much merchandise did she sell that week? © 2009, TESCCC 08/01/09 page 26 of 50