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Chapter 4 Algebra I and Concepts

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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 + 6b) y = 3x – 5c) 2x – 5y = 12

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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 – 5b) y = x + 7c) 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: -2a) m = 6, b = 12

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

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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 + 8c) 5x – 3y = 15

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Day 2: Section 4-1, Horizontal and Vertical Lines Graphing Horizontal Lines 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 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

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Day 2: Section 4-1, Horizontal and Vertical Lines Graph the following lines. First determine if the line is horizontal, vertical, or oblique. 1)y = 42) y = -2x + 43) x = -1

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

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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) 1)Plug the slope in for m 2)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

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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 1)(3, 1), slope 22) (-1, 4), slope -1

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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: 1)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

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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)

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Day 1: Section 4-3, Point-Slope Form Point-Slope Form: given a point, and the slope, an equation can be written such that NameEquationWhen to use it Slope-Intercept Form Point-Slope From Standard FormOnly when converting from a previous form

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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.

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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. 1)y – 3 = 10(x + 4)2) y + 5 = -2(x +6) 3) y + 1 = x – 54) y – 8 = -x

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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)

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

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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.

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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)

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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 StepsExample 1)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

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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)

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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) 3b) -5c) ½ d) -¾

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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 StepsExample 1)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

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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)

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

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

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

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Section 4-5, Scatterplots

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Section 4-5: Scatterplots

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