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Chapter 4

Chapter 4. Algebra I and Concepts. Day 1, Section 4-1: Graphing in Slope-Intercept Form. Slope-Intercept Form: Any equation written in the form y = mx + b m: b: Which of the following are in slope intercept form? Are any in standard form?

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Chapter 4

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  1. Chapter 4 Algebra I and Concepts

  2. Day 1, Section 4-1: Graphing in Slope-Intercept Form Slope-Intercept Form: Any equation written in the form y = mx + b m: b: Which of the following are in slope intercept form? Are any in standard form? a) 4y = 2x + 6 b) y = 3x – 5 c) 2x – 5y = 12

  3. Day 1, Section 4-1: Graphing in Slope-Intercept Form Ex) Identify the slope and the y-intercept of the following equations a) y = ½x – 5 b) y = x + 7 c) 2x – 3y = 12 Ex) Write an equation of a line in slope-intercept form, given the slope and the y-intercept a) Slope: 4, y-intercept: -2 a) m = 6, b = 12

  4. Day 1, Section 4-1: Graphing in Slope-Intercept Form Steps to Graphing an equation in slope-intercept form. Ex) • Plot the ________________ 2) Count the slope ________ over _________, And plot a second point 3) Draw a line connecting The 2 points

  5. Day 1, Section 4-1: Graphing in Slope-Intercept Form Slope Movement Positive Numbers: UP/RIGHT Negative Number: DOWN/LEFT Ex) Graph the following equations using slope-intercept form method a) b) y = 5x + 8 c) 5x – 3y = 15

  6. Day 2: Section 4-1, Horizontal and Vertical Lines Graphing Horizontal Lines Graphing Vertical Lines Equations look like this: x = a number (there is NO y variable) To Graph: 1) Draw a vertical line through that number Graph x = 6 Equations look like this: y = a number (there is NO x variable!) To Graph: 1) Draw a horizontal line through that number Graph y = -2

  7. Day 2: Section 4-1, Horizontal and Vertical Lines Graph the following lines. First determine if the line is horizontal, vertical, or oblique. • y = 4 2) y = -2x + 4 3) x = -1

  8. Day 2: Section 4-1 Write an equation in slope-intercept form for the graph pictured 1) 2) 3)

  9. Day 1, Section 4-2: Writing Equations in Slope-Intercept Form Writing equations in slope-intercept form when given the slope and a point. Steps (USE y = mx + b) Example: slope = 2, (-3, 5) • Plug the slope in for m • Plug the point in for x and y 3) Solve for b 4) Write the equation Using the given m and The b you just found

  10. Day 1, Section 4-2: Writing Equations in Slope-Intercept Form Write a equation for the line using the information given. Use slope-intercept form • (3, 1), slope 2 2) (-1, 4), slope -1

  11. Day 2: Section 4-2, Writing Equations in Slope Intercept Form Write an equation in slope intercept form of a line through the 2 points: (3, 1) and (2, 4) Steps (use y = mx + b) Example: • Use the 2 points and the Slope formula to find m 2) Use m and one point and Plug into y = mx + b to find b 3) Re-write the equation

  12. Day 2: Section 4-2, Writing Equations in Slope Intercept Form Write an equation in slope intercept form of a line through the 2 points: a) (-4, -2) and (-5, -6) b) (-1, 12) and (4, -8)

  13. Day 1: Section 4-3, Point-Slope Form Point-Slope Form: given a point , and the slope, an equation can be written such that

  14. Day 1: Section 4-3, Point-Slope Form Ex) Write an equation in point-slope form for a line that passes through the point (3, -2) and has a slope of ¼ . Then graph the line.

  15. Day 1: Section 4-3, Point-Slope Form Identify the slope and the given point in each of the equations that are in point-slope form. • y – 3 = 10(x + 4) 2) y + 5 = -2(x +6) 3) y + 1 = x – 5 4) y – 8 = -x

  16. Day 1: Section 4-3, Point-Slope Form Graph the equations that are in point-slope form. 1) y – 2 = 3(x + 4) 2) y + 8 = -½ (x – 1)

  17. Day 2: Section 4-3, Re-writing equations Ex) Write in standard form Ex) Write in slope-intercept form

  18. Day 2: Section 4-3, Write an Equation using a Picture of the Graph Write an equation for each line in point-slope form and then convert the equation to slope-intercept form AND standard form.

  19. Day 1: Section 4-4, Parallel Lines Parallel Lines – lines that do not intersect and have the SAME SLOPE! Which of the following lines are parallel? Note: you must be able to identify the slope in each equation! a) b) c) d) e)

  20. Day 1: Section 4-4, Parallel Lines Write an equation in slope-intercept form for the line that passes through (-3, 5) and is parallel to the line y = 2x – 4 Steps Example • Find the slope you need (remember about slopes Of parallel lines!) 2) Use m and the point to Plug into y = mx +b and Solve for b 3) Re-write the equation

  21. Day 1: Section 4-4, Parallel Lines Ex1) Write an equation in slope-intercept form for a line parallel to y = 3x – 5 and through the point (4, -3) Ex2) Write an equation in slope-intercept form for a line parallel to y = -½x + 6 and through the point (-4, 2)

  22. Day 2: Section 4-4 Perpendicular Lines Opposite Reciprocals – 2 numbers whose product is -1. Flip and switch the sign! Perpendicular Lines - Lines that intersect to form a right angle. Perpendicular lines have slopes that are opposite reciprocals. Ex) Find the opposite reciprocals of the following numbers a) 3 b) -5 c) ½ d) -¾

  23. Day 2: Section 4-4 Perpendicular Lines Write an equation in slope-intercept form for the line that passes through (8, 2) and is perpendicular to the line y = -4x + 5 Steps Example • Find the slope you need (remember about slopes Of perpendicular lines!) 2) Use m and the point to Plug into y = mx +b and Solve for b 3) Re-write the equation

  24. Day 2: Section 4-4 Perpendicular Lines Ex1) Write an equation in slope-intercept form for a line perpendicular to y = x + 4 and through the point (3, -2) Ex2) Write an equation in slope-intercept form for a line perpendicular to and through the point (-2, 3)

  25. Day 2: Section 4-4, Comparing Lines Determine if the lines are parallel, perpendicular, or neither. 1) 2) 3) 4)

  26. Section 4-5, Scatterplots Scatterplot – a graph showing the relationship between a set of data with 2 variables

  27. Section 4-5, Scatterplots Ex) What kind of correlation does the graph have? Describe its meaning.

  28. Section 4-5, Scatterplots

  29. Section 4-5: Scatterplots

  30. Section 4-5: Scatterplots

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