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1 NAME DATE PERID - Stud Guide and Intervention Forms of Equations Slope-Intercept Form of a Linear Equation Point-Slope Form of a Linear Equation = m + b, where m is the slope and b is the -intercept - = m( - ), where (, ) are the coordinates of a point on the line and m is the slope of the line Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eample Write an equation in Eample Write an equation in slope-intercept form for the line that has slope - and passes through the point (, 7). slope-intercept form for the line that has slope and -intercept. Substitute for m,, and in the slope-intercept form. = m + b Slope-intercept form 7 = (-)() + b (, ) = (, 7), m = - 7 = - + b Simplif. = b Add to both sides. The -intercept is. The equation in slope-intercept form is = - +. Eercises = m + b Slope-intercept form 0 = ( () + b (, ) = (, 0), m = ) 0 = + b Simplif. - = b Subtract from both sides. The -intercept is -. The slope-intercept form is = -. Write an equation in slope-intercept form for the line described.. slope -, passes through (-, ). slope, -intercept. slope, passes through (, ). slope -, passes through (, -7) Write an equation in slope-intercept form for each graph (, ) (, 0) (0, 0) - - (, ) 8 (-, ) (, ) Lesson - Chapter Glencoe Algebra

2 NAME DATE PERID - Stud Guide and Intervention Parallel and Perpendicular Lines Use the slope-intercept or point-slope form to find equations of lines that are parallel or perpendicular to a given line. Remember that parallel lines have equal slope. The slopes of two perpendicular lines are negative reciprocals, that is, their product is -. Eample Write an equation of the Eample Write an equation of line that passes through (8, ) and is perpendicular to the line whose the line that passes through (-, ) and is parallel to the graph of = +. equation is = - +. The slope of the given line is -. Since the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line is. Use the slope and the given point to write the equation. - = m( - ) Point-slope form - = ( - 8) (, ) = (8, ), m = - = - Distributive Prop. = - Add to each side. An equation of the line is = -. (continued) The slope of the given line is. Since the slopes of parallel lines are equal, the slope of the parallel line is also. Use the slope and the given point to write the equation. - = m( - ) Point-slope form - = ( - (-)) (, ) = (-, ), m = - = + Distributive Prop. = + 8 Add to each side. An equation of the line is = + 8. Eercises Write an equation in slope-intercept form for the line that satisfies each set of conditions.. passes through (-, ), parallel to = +. passes through (, ), perpendicular to = - +. passes through (, -), parallel to the line that passes through (, ) and (, -). passes through (, 7), perpendicular to the line that passes through (, ) and (, ). passes through (8, -), perpendicular to - =. passes through (, -), perpendicular to + = Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 7. passes through (, ), parallel to the line with -intercept - and -intercept 8. passes through (-, ), perpendicular to = - Chapter Glencoe Algebra

3 NAME DATE PERID - Skills Practice Write an equation in slope-intercept form for the line described.. slope, -intercept at -. perpendicular to = -, -intercept at. parallel to = +,. parallel to = - -, passes through (, 7) -intercept at. perpendicular to = - +,. slope, -intercept at -0 passes through (-8, -) 7. parallel to = 9 +, 8. slope, passes through (, ) -intercept at - Write an equation in slope-intercept form for each graph (, ) (0, ) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. (, ) (, ) (, ) Write an equation in slope-intercept form for the line that satisfies each set of conditions.. slope, passes through (, -). slope -, passes through (0, 0). slope -, passes through (0, -). slope, passes through (, 0). passes through (-, -) and (-, ) 7. passes through (-, -) and (, 8) (, ) Lesson - 8. passes through (, 0) and (0, -) 9. passes through (., 0) and (0, ) 0. passes through (, -), perpendicular to the graph of = - -. Chapter Glencoe Algebra

4 NAME DATE PERID - Practice Write an equation in slope-intercept form for the line described.. slope, -intercept at 0. parallel to = +, -intercept at. perpendicular to = +,. parallel to = +, -intercept at passes through (0, 0). perpendicular to = - +,. slope -, -intercept at passes through (, ) Write an equation in slope-intercept form for each graph. 7. (0, ) 8. (, ) 9. (-, ) (0, -) (, -) Write an equation in slope-intercept form for the line that satisfies each set of conditions. 0. slope -, passes through (-, -8). slope, passes through (0, -). slope 0, passes through (0, -0). slope -, passes through (, -8). parallel to = -, -intercept at -. slope, -intercept at -. perpendicular to = - 7. parallel to = - 0, -intercept at 9 passes through (, -) 8. passes through (-8, -7), perpendicular to the graph of = - Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 9. RESERVIRS The surface of Grand Lake is at an elevation of 8 feet. During the current drought, the water level is dropping at a rate of inches per da. If this trend continues, write an equation that gives the elevation in feet of the surface of Grand Lake after das. Chapter Glencoe Algebra

5 NAME DATE PERID - Word Problem Practice. HIKING Tim began a hike near Big Bear Lake, California at the base of the mountain that is 7000 feet above sea level. He is hiking at a stead rate of more feet above sea level per minute. Let A be his altitude above sea level in feet and let t be the number of minutes he has been hiking. Write an equation in slope-intercept form that represents how man feet above sea level Tim has hiked.. CHARITY B midnight, a charit had collected 8 shirts. Ever hour after that, it collected 0 more shirts. Let h be the number of hours since midnight and n be the number of shirts. Write a linear equation in slope-intercept form that relates the number of shirts collected and the number of hours since midnight.. RIGHT TRIANGLES The line containing the base of a right triangle has the equation = +. The leg perpendicular to the base has an endpoint at (, ). What is the slopeintercept form of the equation of the line containing the leg?. DECRATING A group of students is decorating a bulletin board that measures feet b feet. The want to put a line that stretches from the upper right corner to a point feet up along the left edge as shown in the figure. ft ft ft Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. MAPS The post office and cit hall are marked on a coordinate plane. Write the equation of the line in slope-intercept form that passes through these two points. Post ffice - - Cit Hall a. Using the lower left corner of the bulletin board as the origin, what is the equation of the line in slopeintercept form? b. The students change their mind and decide that the line should be lowered b foot. What is the equation of the lowered line in slope-intercept form? c. What are the coordinates of the center of the bulletin board? Does the lowered line pass through the center? Eplain. Lesson - Chapter 7 Glencoe Algebra

6 NAME DATE PERID - Enrichment Two-Intercept Form of a Linear Equation You are alread familiar with the slope-intercept form of a linear equation, = m + b. Linear equations can also be written in the form a + b = with -intercept a and -intercept b. This is called two-intercept form. Eample Draw the graph of - + =. The graph crosses the -ais at - and the -ais at. Graph (-, 0) and (0, ),then draw a straight line through them. - - Eample Write + = in two-intercept form. + = Divide b to obtain on the right side. + = Simplif. The -intercept is ; the -intercept is. Eercises Use the given intercepts a and b, to write an equation in two-intercept form.. a = -, b = -. a =, b = 8. a =, b =. a =, b = 9 Write each equation in two-intercept form. Then draw the graph.. - = -. + = 7. + = -0 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 8 Glencoe Algebra

7 NAME DATE PERID - Spreadsheet Activit Using Linear Equations The slope intercept form of a linear equation is = m + b, where m is the slope and b is the -intercept. Recall that the formula for the slope of a line through (, ) and (, ) is m = - -. You can use the formula for slope and the slope-intercept form to find the value of b. Eample State the slope and -intercept of the graph of the line through (, ) and (, ). Then write an equation of the line in slope-intercept form. Step Use Columns A and B to represent the first point, and Columns C and D to represent the second point on the line. Enter the formula for slope in Column E. Step Substitute one of the given points into the slope-intercept from and solve for b. Since we know the slope of the line, we can solve for b. = m + b Slope-intercept form = m + b Substitute (, ). - m = b Solve for b. Enter this formula into Column F using the names of the spreadsheet cells. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. The slope of the line through (, ) and (, ) is and the -intercept is -. Thus, the equation of the line slopeintercept form is = + (-) or = -. Eercises Use a spreadsheet to find the slope and -intercept of the line through each pair of points. Then write an equation of the line in slope-intercept form.. (0, -), (, ). (, ), (-, -). (-, -), (, ). (-, -9), (8, ). (, 9), (0, 0). (-.,.), (0.9,.9) A B C D Sheet Sheet Sheet E Slope F -intercept - Lesson - 7. Does the spreadsheet work when two points have the same -coordinates? Eplain. Chapter 9 Glencoe Algebra

Investigating Intercepts

Investigating Intercepts Unit: 0 Lesson: 01 1. Can more than one line have the same slope? If more than one line has the same slope, what makes the lines different? a. Graph the following set of equations on the same set of aes.