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Section 3.5

Section 3.5. Slope-Intercept Form. Page 205. Slope-Intercept Form. The line with slope m and y- intercept b is given by y = mx + b, the slope–intercept form of a line. Example. Page 205. For the graph write the slope-intercept form of the line. Solution

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Section 3.5

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  1. Section 3.5 • Slope-Intercept Form

  2. Page 205 Slope-Intercept Form • The line with slope m and y-intercept b is given by • y = mx + b, • the slope–intercept form of a line.

  3. Example Page 205 • For the graph write the slope-intercept form of the line. • Solution • The graph intersects the y-axis at 0, so the y-intercept is 0. • The graph falls 3 units for each 1 unit increase in x, the slope is –3. • The slope intercept-form of the line is y = –3x .

  4. Example Page 206 • Sketch a line with slope 3/4 and y-intercept −2. Write its slope-intercept form. • Solution • The y-intercept is (0, −2). Slope ¾ indicates that the graph rises 3 units for each 4 units run in x. The line passes through the point (4, 1).

  5. Slope-Intercept Form Page 206 Find the slope and y-intercept of the line a. y = 5x – 3 m= 5 y- intercept is (0, -3) c. 7x + y = 6 y = -7x + 6

  6. Example Page 206 • Write the y = 4 – 3x equation in slope-intercept form and then graph it. • Solution • Plot the point (0, 4). • The line falls 3 units for each 1 unit increase in x.

  7. Example #46 Page 212 • Write the y = 1/2x-1 equation in slope-intercept form and then graph it. • Solution • Plot the point (0, -1). • The line rises 1 units for each 2 unit increase in x.

  8. Example #54 Page 212 • Write the -2x-y = -2 equation in slope-intercept form and then graph it. • Solution • Plot the point (0, 2). • The line falls 2 units for each 1 unit increase in x.

  9. Example 5 Page 207-8similar to #73 Homeworktry #74 • Modeling cell phone costs: Roaming with a cell phone costs $5 for the initial connection and $0.50 per minute. • Solution • a. If someone talks for 23 minutes while roaming what is the charge? • b. Write the slope-intercept form that gives the cost of talking for x minutes. • c. If the charge is $8.50, how long did the person talk?

  10. Example 5, cont. Page 207-8similar to #73 Homeworktry #74 • Modeling cell phone costs: Roaming with a cell phone costs $5 for the initial connection and $0.50 per minute. • Solution • c. If the charge is $8.50, how long did the person talk? Person can talk 7 minutes.

  11. Example #74 Page 207-8similar to #73 Homework • Electrical Rates: Electrical service costs $8 per month plus $0.10 per kilowatt-hour of electricity used. • Solution • If the resident of an apartment uses 650 kilowatt-hours in 1 month, what is the charge? • Write an equation in slope-intercept form that gives the cost C. • If the monthly electrical bill for the apartment’s resident is $43, how many kilowatt-watt hours were used?

  12. Example #74, cont. Page 207-8similar to #73 Homeworktry #74 • Modeling cell phone costs: Roaming with a cell phone costs $5 for the initial connection and $0.50 per minute. • Solution • c. If the monthly electrical bill for the apartment’s resident is $43, how many kilowatt-watt hours were used? 350 kilowatt-hours used.

  13. Page 208-10 Parallel and Perpendicular Lines

  14. Example Page 208-10 • Find the slope-intercept form of a line parallel to y = 3x + 1 and passing through the point (2, 1). Sketch a graph of each line. • Solution • The line has a slope of 3 any parallel line also has slope 3. • Slope-intercept form: y = 3x + b. The value of b can be found by substituting the point (2, 1) into the equation.

  15. Parallel Lines Page 208-10 Show that the line passing through (4,2) and (6,6) is parallel to the line passing through (0,-2) and (1,0). Slopes are equal

  16. Example Page 208-10 • Find the slope-intercept form of a line passing through the origin that is perpendicular to each line. • a. y = 4x b. • Solution • a. The y-intercept is 0. • Perpendicular line has a slope of • b. The y-intercept is 0. • Perpendicular line has a slope of

  17. Perpendicular Lines Page 208-10 Show that the line passing through (-1,4) and (3,2) is perpendicular to the line passing through (-2,-1) and (2,7).

  18. Example Page 208-10 • Find the slope-intercept form of the line perpendicular to • and passing through the point (1, 0). Sketch each line in the same xy-plane. • Solution • A line perpendicular has slope –3. • The value of b can be found by substituting the point in the slope-intercept form.

  19. DONE

  20. Objectives • Basic Concepts • Finding Slope-Intercept Form • Parallel and Perpendicular Lines

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