Understanding Slope-Intercept Form and Graphing Techniques
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This chapter explores the fundamental concepts of graphing equations in slope-intercept form (y = mx + b), where 'm' represents the slope and 'b' the y-intercept. Learn to identify equations in slope-intercept and standard forms, and practice finding slopes and y-intercepts for various equations. The chapter also covers the steps for graphing, including plotting points using slope, as well as horizontal and vertical lines. Additionally, discover the characteristics of parallel and perpendicular lines, and how to interpret scatterplots.
Understanding Slope-Intercept Form and Graphing Techniques
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Presentation Transcript
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? a) 4y = 2x + 6 b) y = 3x – 5 c) 2x – 5y = 12
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
Day 1: Section 4-1 Write an equation in slope-intercept form for the graph pictured 1) 2) 3)
Day 2, 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
Day 2, 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
Day 3: 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
Day 3: 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
Day 1: Section 4-4, Parallel Lines Parallel Lines – lines that do not intersect and have the SAME SLOPE! Ex) Use the 3 graphs to determine by looking if the lines are parallel
Day 1: Section 4-4, Parallel Lines Which of the following lines are parallel? Note: you must be able to identify the slope in each equation! a) b) c) d) e)
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
Day 2: Section 4-4, Comparing Lines Determine if the lines are parallel, perpendicular, or neither. 1) 2) 3) 4)
Section 4-5, Scatterplots Scatterplot – a graph showing the relationship between a set of data with 2 variables
Section 4-5, Scatterplots Ex) What kind of correlation does the graph have? Describe its meaning.
