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5-5 Slope-Intercept Form Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

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5-5 Slope-Intercept Form Warm Up Find each y-intercept. 1. y = 3x x – 3y = 12 Find each slope. 6. 3x + 2 = 6y Solve each equation for y. 4. 6x + 2y = 6 –4 –3

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5-5 Slope-Intercept Form 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequalities (e.g., they sketch the region defined by 2x + 6y < 4). California Standards

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5-5 Slope-Intercept Form Additional Example 3C: Using Slope-Intercept Form to Graph Write the equation in slope-intercept form. Then graph the line described by the equation. 2y + 3x = 6 Step 1 Write the equation in slope-intercept form by solving for y. 2y + 3x = 6 –3x –3x 2y = –3x + 6 Subtract 3x from both sides. Since y is multiplied by 2, divide both sides by 2.

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5-5 Slope-Intercept Form Additional Example 3C Continued Step 2 Graph the line. slope: m = y-intercept: b = 3 Plot (0, 3). Count 3 units down and 2 units right and plot another point. Draw the line connecting the two points. Write the equation in slope-intercept form. Then graph the line described by the equation. is in the form y = mx + b.

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5-5 Slope-Intercept Form Additional Example 3B: Using Slope-Intercept Form to Graph Write the equation in slope-intercept form. Then graph the line described by the equation. y = 2 y = 0x + 2 is in the form y = mx + b slope: m = 0 y-intercept: b = 2 Step 1 Plot (0, 2). Step 2 For any value of x, y will equal 2. Plot 2 additional points. Step 3 Draw the line connecting the points.

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5-5 Slope-Intercept Form Check It Out! Example 3a y-intercept: b = 0 Plot (0, 0). Count 2 units up and 3 units right and plot another point. Draw the line connecting the two points. slope: Write the equation in slope-intercept form. Then graph the line described by the equation. y = x + 0 is in the form y = mx + b.

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5-5 Slope-Intercept Form Check It Out! Example 3b 6x + 2y = 10 Step 1 Write the equation in slope intercept form by solving for y. 6x + 2y = 10 –6x –6x 2y = –6x + 10 Subtract 6x from both sides. Since y is multiplied by 2, divide both sides by 2. Write the equation in slope-intercept form. Then graph the line described by the equation. y = –3x + 5

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5-5 Slope-Intercept Form Check It Out! Example 3b Continued Step 2 Graph the line. y-intercept: b = 5 Plot (0, 5). slope: m = Count 3 units down and 1 unit right and plot another point. Draw the line connecting the two points. Write the equation in slope-intercept form. Then graph the line described by the equation. y = –3x + 5 is in the form y = mx + b.

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5-5 Slope-Intercept Form Check It Out! Example 3c y = –4 Step 1 Plot (0, –4). y = –4 is in the form y = mx + b. y-intercept: b = –4 slope: m = 0 = = 0 Since the slope is 0, the line will be horizontal at y = –4. Write the equation in slope-intercept form. Then graph the line described by the equation.

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5-5 Slope-Intercept Form Additional Example 4: Application A closet organizer charges a $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below.

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5-5 Slope-Intercept Form Additional Example 4 Continued a. Write an equation that represents the cost as a function of the number of hours. An equation is y = 30h A closet organizer charges $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below. Costis $30 per hour timesplus $100. y = hours h

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5-5 Slope-Intercept Form Additional Example 4 Continued b. Identify the slope and y-intercept and describe their meanings. The y-intercept is 100. This is the cost for 0 hours, or the initial fee of $100. The slope is 30. This is the rate of change of the cost: $30 per hour. c. Find the cost if the organizer works 12 hrs. y = 30h = 30(12) = 460 Substitute 12 for h in the equation. The cost of the organizer for 12 hours is $460.

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5-5 Slope-Intercept Form Check It Out! Example 4 A caterer charges a $200 fee plus $18 per person served. The cost as a function of the number of guests is shown in the graph. a. Write an equation that represents the cost as a function of the number of guests. An equation is y = 18m Costis $18 per person times plus $200. y = meals m

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5-5 Slope-Intercept Form Check It Out! Example 4 Continued b. Identify the slope and y-intercept and describe their meanings. The y-intercept is 200. This is the cost for 0 people, or the initial fee of $200. The slope is 18. This is the rate of change of the cost: $18 per person. c. Find the cost of catering an event for 200 guests. y = 18m = 18(200) = 3800 Substitute 200 for m in the equation. The cost of catering for 200 people is $3800.

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5-5 Slope-Intercept Form Lesson Quiz: Part II Write each equation in slope-intercept form. Then graph the line described by the equation. 4. 6x + 2y = 10 y = –3x x – y = 6 y = x – 6

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