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Cognitive Algebra Name________ Date_____ 5.5 Notes: Point slope of a linear equation • I can state the point-slope form of an equation. • I can write equations in point-slope form. A. Graph the line that passes through the point (1, 4) and has a slope of 2. B. On the same coordinate plane, graph the equation y – 4 = 2(x – 1). C. What is true about the two lines? D. How is the ordered pair related to the equation in Part B? E. How is the slope related to the equation in part B? Cognitive Algebra Name________ Date_____ 5.5 Notes: Point slope of a linear equation F. Graph the line that passes through the point (-2, 3) and has a slope of -3. G. On the same coordinate plane, graph the equation y – 3(x + 2). H. What is true about the two lines? I. How is the ordered pair related to the equation in Part G? J. How is the slope related to the equation in part G? 10 8 6 4 (x, y) 2 (x1, y1) -10 -5 5 -2 -4 10 Cognitive Algebra Name________ Date_____ 5.5 Notes: Point slope of a linear equation Examples 1. Write an equation of the line. Use the points (-2, 3) & (-1, 1). Write your equation in point slope-form. 2. Write an equation of the line. Write the answer in slope-intercept form. 3. Guided Practice: Write an equation of the line in point-slope form that passes 1 through the point (-1, -6) with slope − . 3 Cognitive Algebra Name________ Date_____ 5.5 Notes: Point slope of a linear equation Example: The information below was taken from an article that appeared in a newspaper. 4. Use the information to write a linear model for optimal running pace. 5. Use the model to find the optimal running pace for a temperature of 80°F. Guided Practice. 6. A crate can hold up to 30 oranges. The crate with 16 oranges weighs 8.8 lb. Assuming that each orange weighs about 0.4 lb, write a linear model to represent the weight of the crate with x oranges. How much will a full crate weigh? 7. Name the following form of the equation of a line: y − y1 = m ( x − x1 ) . Cognitive Algebra Name________ Date_____ 5.5 Notes: Point slope of a linear equation 8. What are the values of m, x1 , and y1 in the equation y – (-1) = 3(x – 2)? Write an equation of the line in point-slope form. 9. 10. Write an equation of the line in point-slope form that passes through the given point and has the given slope. 11. (-5, -7), m = -2. 12. (7, -7), m = -8 Write an equation of the line in point-slope form that passes through the given points. 13. (-17, -8) and (-7, -5) 14. (-4, -7) & (2, 2) Eosophobia is the fear of dawn