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# A1 Chapter 5 Study Guide

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• 1. Algebra 1 Chapter 5 Study Guide What is slope-intercept form? _______________________________________________ What is point-slope form? __________________________________________________ What is standard form? ____________________________________________________ What is the equation for slope given 2 points? __________________________________ Write an equation of the line in slope-intercept form. 1. The slope is 1; the y-intercept is 2. 2. The slope is – ¼; the y-intercept is 1. 3. The slope is – 3; the y-intercept is – ½. 4. 5. Using Point-Slope form: Write an equation given POINT and SLOPE. Step 1)Plug in the slope and the point. Remember: points are written (x, y). Step 2)Distribute the slope. Step 3)Combine like terms. 6. m = – 2, (6, – 3) 7. m = 1/3, (– 3, 0) 8. m = – 3, (– 2, – 1) Extra practice p. 282 (12 – 29) Parallel and Perpendicular What does parallel mean? __________________________________________________ What does perpendicular mean? _____________________________________________ If you are given an equation, and told to find a DIFFERENT equation that is parallel, use the slope from the original equation. If you are also given a POINT, use point-slope form to find the new equation. 9. Find an equation parallel to y = 2/3 x – 2 that goes through (– 2, 1). 10. Find an equation parallel to y = – 3x – 2 that goes through (3, – 4). 11. Find an equation perpendicular to y = 2/3 x – 2 that goes through (– 2, 1). 12. Find an equation perpendicular to y = – 3x – 2 that goes through (3, – 4). Extra practice p. 283 (32 – 40) and 289 (45 – 47)
• 2. Write an equation given 2 POINTS. Step 1)Find slope using the slope equation. Step 2)Use the slope and one of the points in the point-slope form equation, follow steps above. 13. (1, 6) and (3, – 4) 14. (– 3, 1) and (5, 5) 15. (2, 4) and (1, – 2) 16. (– 8, – 4) and (4, 2) 17. (12, 2) and (7, 2) Extra practice p. 288 (18 – 35) Fitting a Line to Data Step 1)Make a scatter plot from the data. Step 2)Draw a straight line through the points. Step 3)Choose 2 points on the line and make an equation. 18. A tadpole eventually turns into a frog. There is a relationship between the age of a tadpole and the length of its tail (which eventually disappears). Make a scatter plot of the data and write an equation of the line of best fit. Age (days) Length of Tail (mm) 5 14 2 15 9 3 7 8 12 1 10 3 3 12 6 9 19. Draw a scatter plot and find the equation of the line of best fit. What kind of correlation does this data have? x 2 9 1 8 5 y 11 27 9 23 17 Standard Form --No fractions. Multiply all terms by denominator to get rid of fractions. --x and y on the same side of the equal sign. 20. Write y = 2/5 x – 3 in standard form. 21. Write the equation of m = – 2, (– 4, 3) in standard form. 22. Write – 5x + 11 = ½ y in standard form. Extra practice p. 311 (18 – 44) Does this have a positive correlation? negative correlation? no correlation?
• 3. Linear Models Given a set of data, graph the line of best fit and find its equation. What does interpolation mean? ______________________________________________ What does extrapolation mean? ______________________________________________ 23. Graph both sets on different grids. Which is a linear model? set 1 x 1 2 3 4 y 12 25 36 48set 2
• 4. 24. Use the table to do the following: (amount spent on sports supplies each year) Years since 1990 Billions of Dollars 0 31.6 1 32.8 2 ? 3 36.5 4 40.1 5 42.7 a) Write a linear equation to represent the amount spent on sports supplies. b) Estimate the amount spent in 1992. Is this interpolation or extrapolation? c) Estimate the amount spent in 2005. Is this interpolation or extrapolation? Extra practice p. 319 (11 – 34) 25. What is the equation of the line that passes through (7, 4) and (– 5, – 2)? [A] y = ½ x – ½ [B] y = – ½ x + ½ [C] y = – ½ x – ½ [D] y = ½ x + ½ 26. Choose the lines that are perpendicular. Line p that passes through (4, 0) and (6, 4). Line q that passes through (0, 4) and (6, 4). Line r that passes through (0, 4) and (0, 0). [A] line p and line q. [B] line p and line r. [C] line q and line r. [D] none of these. All students in a class were surveyed about how long they studied at home. The table shows hours studied and average test grades. Hours spent studying 0 . 25 .5 . 75 1 1. 5 2 3 5 7 Average grade on test 2 9 32 3 5 38 4 0 47 5 4 6 6 7 9 89 27. Make a scatter plot of the data. 28. Make a line of best fit and give the equation for it. 29. If you study 4 hours, what is your expected test grade? 30. If you want to make a 93, how long should you study? 31. If you were a parent, what advice would you give your child about studying at home for this test? Explain your reasoning. x 1 2 3 4 y 10 5 2 1