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Moving Straight Ahead

Moving Straight Ahead. Students will work on linear equations, solving equations, solving inequalities, determining slopes and what they mean, and determining the intersection of 2 lines. Investigation 4. Students will be exploring slope and connecting it again to rates and ratios. Vocab.

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Moving Straight Ahead

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  1. Moving Straight Ahead Students will work on linear equations, solving equations, solving inequalities, determining slopes and what they mean, and determining the intersection of 2 lines.

  2. Investigation 4 Students will be exploring slope and connecting it again to rates and ratios.

  3. Vocab Slope rise over the run change in y / change in x (y-y)/(x-x) Parallel Lines two lines that never touch, same slope Perpendicular Lines two lines that intersect and form a 90 degree angle, slopes are opposite reciprocals

  4. Homework Pg 98 A 2, 7, 8-12, 16,17,20-22,29,35 B 7,8-12, 18,19,20-22,29,36,40

  5. Invest 4.1 and 4.2Using Rise and RunFinding Slope of a line How is the steepness of a set of stairs related to a straight-line graph? How can you find the y-intercept and the slope of a line from data in a table, graph or equation?

  6. NOTES To calculate the slope – this should always be in simplest fractional form, no decimals or mixed numbers, unless dollars Graph: Draw a triangle on the top of the graph like a set of stairs Get the rise of the triangle and the run, write as a fraction Table and Graph: Pick two points and sub into equation

  7. NOTES Y-intercept When x=0 You could make a table Or Write what you know in the equation Sub in a point from the line and solve for b y = mx + b

  8. Examples Using Ratios and Rates When thinking of stairs If the ratio of rise to run for each step should be between 9/20 and 3/5 and the rise plus the run should be between 17 and 17.5 inches If a set of stairs is being built and the ratio of rise to run is 3 to5 • Is this ratio within the carpenters guidelines? • Write an equation that would represent this • If the rise of a stair is 8 inches what should the run be and does this fit the guidelines?

  9. Calculate the slope, y-int and write the equation The points (3,4) and (-2, -10) lie on a line

  10. Invest 4.3Exploring Patterns with Lines How can you predict whether two lines are parallel or perpendicular form their equations?

  11. NOTES Writing a line that is parallel Use same slope but a different y-int of b value Writing a line that is perpendicular Use opposite reciprocal slopes and same or different y-int

  12. Example Are the lines parallel or perpendicular, explain Given the lines write the equation of a line that is parallel and perpendicular to the given line Y = 4x – 3 y = -2/3x + 1

  13. Invest 4.4Writing Equations for Linear Relationships What information do you need to write an equation for a linear relationship? Is the expression for dependent variable always the same?

  14. NOTES What is given What do you need to find Show work to get your calculations/equaions

  15. Example Today is Chantal’s birthday. Her grandfather gave her some money as a birthday gift. Chantel plans to put her birthday money in a safe place and add part of her allowance to it each week. Her sister, Chanice, wants to know how much her grandfather gave her and how much of her allowance she is planning to save each week. As usual, Chantel does not answer her sister directly. Instead, she wants to her to figure out the answer herself. She gives her these clues: After 5 weeks she will have $175 After 8 weeks she will have $190 • Write an equation to represent this situation • How much of her allowance does she save each week? • How much did her grandpa give her?

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