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Copyright © 2013 Pearson Education, Inc. Section 3.5 Slope-Intercept Form
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The line with slope m and y-intercept b is given by y = mx + b, the slope–intercept form of a line. Slope-Intercept Form Page 205
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Example 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. Page 205
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Example 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). Page 206
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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 Slope-Intercept Form Page 206
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Example 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. Page 206
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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. Example #46 Page 212
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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. Example #54 Page 212
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Example 5 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? Page 207-8 similar to #73 Homework try #74
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Example 5, cont. 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? Page 207-8 similar to #73 Homework try #74 Person can talk 7 minutes.
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Example #74 Electrical Rates: Electrical service costs $8 per month plus $0.10 per kilowatt-hour of electricity used. Solution a. If the resident of an apartment uses 650 kilowatt-hours in 1 month, what is the charge? b. Write an equation in slope-intercept form that gives the cost C. c. If the monthly electrical bill for the apartment’s resident is $43, how many kilowatt-watt hours were used? Page 207-8 similar to #73 Homework
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Example #74, cont. 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? Page 207-8 similar to #73 Homework try #74 350 kilowatt-hours used.
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Parallel and Perpendicular Lines Page 208-10
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Example 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. Page 208-10
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Show that the line passing through (4,2) and (6,6) is parallel to the line passing through (0,-2) and (1,0). Parallel Lines Page 208-10 Slopes are equal
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Example Find the slope-intercept form of a line passing through the origin that is perpendicular to each line. a. y = 4xb. 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 Page 208-10
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Show that the line passing through (-1,4) and (3,2) is perpendicular to the line passing through (-2,-1) and (2,7). Perpendicular Lines Page 208-10
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Example 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. Page 208-10
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DONE
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Objectives Basic Concepts Finding Slope-Intercept Form Parallel and Perpendicular Lines
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