Report

Lesson 5-4 Point-Slope Form Sept. 22, 2014 Daily Learning Target • I will write and graph linear equations using point-slope form. What is it? y – y1 = m(x – x1) m = slope (x1, y1) = a point the line goes through. Here is how it works!! • Given a point (x1, y1) on a line and the line’s slope m, you can use the definition of slope to derive point-slope form. y2 – y1 • Definition of slope (m) = x2 – x1 • Let (x, y) be any point on the line. Substitute for (x, y) for (x2, y2). y – y1 • =m x – x1 How it works cont. y – y1 • =m x – x1 • Multiply both sides by x – x1 y – y1 = m(x – x1 ) point-slope form m = slope (x1, y1) = a point the line goes through. Example 1 • A line passes through (-3, 6) and has slope -5. What is an equation of the line in point slope form? **Remember: y – y1 = m(x – x1 ) y – 6 = -5(x + 3 ) You Try It 2 . 3 • A line passes through (8, -4) and has slope What is an equation in point-slope for of the line? y+4= 2 (x 3 – 8) Example 2 • What is the graph of the equation y–1= 2 (x 3 – 2) What is the slope? What is the point it passes through? You Try • What is the graph of the equation: a. y + 7 = - 4 (x 5 – 4) b. y – 1 = -3(x + 2) c. y – 2 = 4 (x 9 – 3) Example 3 • What is an equation of the line from the coordinate plane? Steps to think about: • Think --You need the slope m, so start with the slope formula. – Use the given points to find the slope – Use point-slope form – Use either point for (x1, y1). You Try • Use the same procedure as the example to write the equation for a graph where the line goes through points (-3, 4) and (1, 1). y–1=- 3 (x 4 – 1) Example 4 • The table shows the altitude of a hot-air balloon during its linear descent. What equation in point-slope form. What does it look like in slope-intercept form? • PSF: y – 640 = -2.5(x – 10) • SIF: y = -2.5x + 665 Time, x (s) Altitude, y (m) 10 640 30 590 70 490 90 440 You Try • The table shows the number of gallons of water, y, in a tank after x hours. The relationship is linear. What is an equation in point-slope forms that models that data. What does the slope Time, x (h) Water, y (gal) represent? 2 3320 PSF: y – 3320 = 1250(x – 2); 3 4570 The rate at which water is 5 7070 8 10,820 being added to the tank. Homework • Workbook: • Page 151 problems 1, 3, 4, 6, 7, 8, 10, 11, 13 • Page 153 problems 1-6 ALL