Investigating Intercepts

Transcription

1 Unit: 0 Lesson: 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. Label each graph. i. = ii. = - 1 iii. = + iv. = v. = b. What observations can ou make about the lines? c. What is the slope of all the lines? d. How does addition or subtraction of a b value change the line? e. What is the name of b? f. Predict the graph of 7. Sketch our prediction on the above graph. Use the graphing calculator to verif our prediction. g. Complete the sentence: Lines with the same slope are. 01, TESCCC 07/1/1 page 1 of 7

2 Unit: 0 Lesson: 01 Finding Intercepts In a function an intercept is the point at which a line crosses an ais. If it crosses the -ais, it is called the and the point is (0, ). If it crosses the -ais, it is called the and the point is (, 0). The -intercepts are also known as the, because the -intercepts are where the value of the function is zero. Finding intercepts from a graph. Stud the graphs of the lines below. Eamples: a. b intercept: -intercept: -intercept: -intercept: 01, TESCCC 07/1/1 page of 7

3 Unit: 0 Lesson: 01 Finding intercepts from a table -intercept -intercept zero of function (0, ) (, 0) 0 0 Use patterns to complete the tables and find intercepts a. Determine the slope a. Determine the slope b. Circle the -intercept (zero of function) b. Complete the pattern to find where = 0. c. Circle the -intercept (zero of function) c. Write the coordinates of the - intercept. d. Write the coordinates of the -intercept e. Complete the pattern to find where = 0. d. Circle the -intercept f. Circle the -intercept g. Write the coordinates of the -intercept e. Write the coordinates of the - intercept 01, TESCCC 07/1/1 page 3 of 7

4 Unit: 0 Lesson: 01 Finding intercepts from an equation One form of linear equations is called the form. An linear function can be written in this form in order to determine the slope and -intercept. m b or f( ) m b m represents. b represents. Use algebraic manipulation to transform the following equation to the slope-intercept form. Determine the slope and -intercept form of the function. 3 = 9 Solve for. 5. Find the slope and -intercept for each function. a. = b. f() = 1 35 c. = 0 d. 3 + = 5 e. = 1 Special Cases: Find the slope and -intercept.. = 7. = 01, TESCCC 07/1/1 page of 7

5 Unit: 0 Lesson: 01 Practice Problems 1. Find the slope and the - intercept and -intercept of the following graphs of lines. a. b intercept (zero of function) -intercept intercept (zero of function) -intercept c. d intercept (zero of function) -intercept intercept (zero of function) -intercept 01, TESCCC 07/1/1 page 5 of 7

6 Unit: 0 Lesson: 01 Find the slope and intercepts from the data in the tables intercept (zero of function) -intercept -intercept (zero of function) -intercept Find the slope and -intercept of each equation.. = f( ) = 1 3. = =. 5 = = = - 01, TESCCC 07/1/1 page of 7

7 Unit: 0 Lesson: A line contains the points (-, -5) and (3, 1). a. Sketch a graph of the line. b. What is the slope of the original line? c. If the slope is multiplied b 3 and the -intercept stas the same, sketch a transformed graph on the same coordinate plane of the resulting line. d. What is the slope of the transformed line? 1. A line with a slope of one-half, contains the point (-, -5). a. Sketch a graph of the line. b. What is the -intercept of the original line? c. If the slope remains the same and the -intercept increased b 3 units, sketch a transformed graph on the same coordinate plane of the resulting line. d. What is the -intercept of the transformed line? e. How would ou describe the relationship between the two lines? Eplain. 01, TESCCC 07/1/1 page 7 of 7