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Lesson 5-4

Lesson 5-4. Writing Equations in Slope-Intercept Form. Transparency 4. Click the mouse button or press the Space Bar to display the answers. Transparency 4a. Objectives. Write an equation of a line given the slope and one point on a line

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Lesson 5-4

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  1. Lesson 5-4 Writing Equations in Slope-Intercept Form

  2. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 4a

  4. Objectives • Write an equation of a line given the slope and one point on a line • Write an equation of a line given two points on a line

  5. Vocabulary Linear extrapolation – the use of a linear equation to predict values that are outside the data range

  6. y y x x x-y Coordinate Plane Point Plotting Quadrants II I up 7 left 4 right 5 III IV down 8 (x, y) (-4, 7) (5, -8) x – left or right y – up or down

  7. Slope-intercept form Replace m with ½ ,y with –3, and x with 2. Multiply. Subtract 1 from each side. Simplify. Example 1 Write an equation of a line that passes through (2, –3)with slope ½ Step 1The line has slope ½ To find the y-intercept,replace m with ½ and (x, y) with (2, –3) in theslope-intercept form. Then, solve for b.

  8. Step 2Write the slope-intercept form using Slope-intercept form Replace m with and b with –4. Answer: The equation is Example 1 cont Using your calculator to graph it and the CALC menu to verify that it passes through (2, –3).

  9. Example 2 Economy In 2000, the cost of many items increased because of the increase in the cost of petroleum. In Chicago, a gallon of self-serve regular gasoline cost $1.76 in May and $2.13 in June. Write a linear equation to predict the cost of gasoline in any month in 2000, using 1 to represent January. Explore You know the cost of regular gasoline in May and June. Plan Let x represent the month and yrepresent the cost of gasoline that month. Write an equation of the line that passes through (5, 1.76) and(6, 2.13).

  10. Slope formula Letand . Simplify. Example 2 cont Solve Find the slope.

  11. Slope-intercept form Replace m with 0.37, x with 5, and y with 1.76. Replace m with 0.37 and b with –0.09. Multiply. Answer: The equation is Subtract 1.85from each side. Simplify. Example 2 cont Choose (5, 1.76) and find the y-intercept of the line.

  12. Economy The Yellow Cab Company budgeted $7000 for the July gasoline supply. On average, they use 3000 gallons of gasoline per month. Use the prediction equation where x represents the month and y represents the cost of one gallon of gasoline, to determine if they will have to add to their budget. Explain. Original equation Replace x with 7. Simplify. Example 3 Answer: If gas increases at the same rate, a gallon of gasoline will cost $2.50 in July. 3000 gallons at this price is $7500, so they will have to add $500 to their budget.

  13. Summary & Homework • Summary: • To write an equation given the slope and one point, substitute the values of m, x, and y into the slope-intercept form and solve for b. Then write the slope-intercept form using the values of m and b • To write an equation given two points, find the slope. Then follow the steps above • Homework: • Pg 284 12-32 even

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