Point-Slope Form of an Equation
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1 Name: Date: Page 1 of 9 Point-Slope Form of an Equation 1. Graph the equation = + 4 b starting at (0,4) and moving to another point on the line using the slope. 2. Now draw another graph of = + 4. This time pick the point ( 8, 2) which is a point on the line, and use slope to count up and right from that point to find other points on the graph. Do ou end up with the same line as ou did in part 1a above? 3. Notice that ou can find points on a line or graph a line b starting at a point and moving according to the slope. Does it matter which point on the line is chosen to start with? Activit CT Algebra I Model Curriculum Version 3.0
2 Name: Date: Page 2 of 9 Facts about Point-Slope Form The point-slope form of a line is a special form that tells ou the of a line and on the line. The point-slope formula is: m is the is the is the is the is the Point-slope form comes from When ou substitute the values of the specific point (, ) into the point slope formula, ou will obtain a true statement 0=0 which proves that (, ) is a point on the line. The slope-intercept form of a line is = m + b. m is the same value in both forms. Notice that it is the coefficient of the variable. EXAMPLE: For the equation 7 = ( 2), the particular point is (2,7). The -coordinate of this point is 2 and the -coordinate of this point is 7. The line has slope of. 4. Verif that (2,7) is a solution to the equation 7 = ( 2) b evaluating the equation when =2 and =7. 5. For each equation in point-slope form, identif the particular point and the slope. Then graph each equation. Test our point in the equation to be sure that the point makes the equation true. Activit CT Algebra I Model Curriculum Version 3.0
3 Name: Date: Page 3 of 9 a. 3 = ( 1) b. 8 = ( 2) Activit CT Algebra I Model Curriculum Version 3.0
4 Name: Date: Page 4 of 9 c. 2 = ( ( 5)) d. + 6 = ( + 2) Activit CT Algebra I Model Curriculum Version 3.0
5 Name: Date: Page 5 of 9 6. Use the point and the slope to write an equation of the line in point-slope form. = m( ) a. (3,5), m = 2 b. (2,6), m = c. (3,0), parallel to the line = d. (0,4), perpendicular to the line = + 2 e. (3,2), m = 0 f. (-3,2), m = g. (-5,-1), m=3 Activit CT Algebra I Model Curriculum Version 3.0
6 Name: Date: Page 6 of 9 7. Plot the two points ( 3,7) and (1, 3). Draw the line containing the two points. What is the slope between the two points? Write an equation in point-slope form: 8. Find an equation of the line between the given two points b first finding the slope, then finding the point-slope form of the equation. a. through points (5,8) and ( 2, 7) b. through points ( 2, -6) and ( 7, 5) Activit CT Algebra I Model Curriculum Version 3.0
7 Name: Date: Page 7 of 9 9. This Februar and March, the middle school students had their most successful food drive, topping last ear s total b 57 items. The started the food drive on da 0 with 8 cans of fruit juice which had been donated too late to be included in the November food drive. Contributions poured in at a constant rate of 12 food items per da. B the time the drive was over, the cans covered the cafeteria stage. a. What is the dependent variable? b. What is the independent variable? c. Find the slope described in the situation. d. Find a point described in the situation. e. Write an equation of the line in point-slope form. f. Write an equation of the line in slope-intercept form. g. Use either equation to tell how man food items had been collected b the 10 th da. h. Use either equation to tell how man das it took to collect 488 items Activit CT Algebra I Model Curriculum Version 3.0
8 Name: Date: Page 8 of 9 Transforming a function from point-slope form into slope-intercept form 10. a. Sketch the graph of the function 2 = 4( 3). b. Transform the previous equation into slope intercept form b appling the distributive propert on the right side and solving for. c. What are the slope and -intercept? d. Confirm that the equation in slope-intercept form gives the same graph as the equation in point-slope form. Activit CT Algebra I Model Curriculum Version 3.0
9 Name: Date: Page 9 of a. Sketch the graph of the function + 4 = ( + 6). b. Transform the previous equation into slope-intercept form b appling the distributive propert on the right side and solving for. c. What are the slope and -intercept? d. Confirm that the equation in slope-intercept form gives the same graph as the equation in point-slope form. Activit CT Algebra I Model Curriculum Version 3.0
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