3-4 Slope-Intercept Form. State the slope and the y-intercept for the graph of each equation. 1. y = 3x + 4 ANSWER: 3; 4. 2.
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1 State the slope and the y-intercept for the graph of each equation. 1. y = 3x + 4 3; 4 Write an equation in slope-intercept form for the graph shown y = x ; 3. 3x + y = 4 3; 4 Write an equation of a line in slope-intercept form with the given slope and y-intercept slope:, y-intercept: 2 5. slope:, y-intercept: 8 esolutions Manual - Powered by Cognero Page 1
2 8. The Viera family is traveling from Philadelphia to Orlando for vacation. The equation y = 1,000 65x distance in miles remaining in their trip after x hours. a. Graph the equation. b. Interpret the slope and the y-intercept. 10. y = x + a. 11. y = x + 1 b. The driving rate, 65 mph; the distance from which they began their trip, 1,000 miles. Copy and Solve Graph each equation on a separate piece of grid paper. 9. y = x Model with Mathematics Refer to the graphic novel frame below for Exercises a b. a. Write an equation in slope-intercept form for the total cost of any number of tickets at 7 tickets for $5. b. Write an equation in slope-intercept form for the total cost of a wristband for all you can ride. a. y = $0.71x b. y = $25 esolutions Manual - Powered by Cognero Page 2
3 13. Persevere with Problems The x-intercept is the x-coordinate of the point where a graph crosses the x-axis. What is the slope of a line that has a y- intercept but no x-intercept? Explain. 0; Sample answer: 0; A line that has a y-intercept but no x-intercept is a horizontal line. 14. Reason Abstractly Write an equation of a line that does not have a y-intercept. Sample answer: x = Justify Conclusions Suppose the graph of a line has a negative slope and a positive y-intercept. Through which quadrants does the line pass? Justify your reasoning. Quadrants I, II, and IV; if a y-intercept is graphed at (0, b), where b is positive, and then a line is drawn through the point so that it has a negative slope, the line will pass through Quadrants I, II, and IV. 16. Make a Conjecture Describe what happens to the graph of y = 3x + 4 when the slope is changed to. Sample answer: The graph becomes less steep. Write an equation of a line in slope-intercept form with the given slope and y-intercept. 20. slope:, y-intercept: slope: 2, y-intercept: slope:, y-intercept: 23. Persevere with Problems The equation y = 15x + 37 can be used to approximate the temperature y in degrees Fahrenheit based on the number of chirps x a cricket makes in 15 seconds. Graph the equation to estimate the number of chirps a cricket will make in 15 seconds if the temperature is 80 F. State the slope and the y-intercept for the graph of each equation. 17. y = 5x + 2 5; y = x 6 ; about 3 chirps ; y 2x = 8 2; 8 esolutions Manual - Powered by Cognero Page 3
4 24. The Lakeside Marina charges a $35 rental fee for a boat in addition to charging $15 an hour for usage. The total cost y of renting a boat for x hours can be represented by the equation y = 15x a. Graph the equation. b. Interpret the slope and the y-intercept. a. $80; 26. The table shows Mr. Blackwell s total earnings as a car salesman for different sale amounts. Graph the points on the coordinate plane and connect them with a straight line. b. the hourly rental charge, $15, and the base rental fee, $ Write an equation in slope-intercept form for the table shown. Write an equation in slope-intercept form to represent the relationship. y = 8x + 5 y = 125x esolutions Manual - Powered by Cognero Page 4
5 27. Jaquie has 20 postcards in her collection. Each time she goes on vacation she buys 8 postcards to add to the collection. The total number of postcards y can be represented by the equation y = 8x Complete the following statements regarding the line. The slope of the line is and the y-intercept is. The number of postcards when she began collecting and the number of postcards added each vacation. The slope of the line is and the y-intercept is. The number of postcards when she began collecting and the number of postcards added each vacation. Solve each equation for d when c = c + 4d = c 6d = 24 4 esolutions Manual - Powered by Cognero Page 5
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