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3-4 Equations of Lines

3-4 Equations of Lines. You found the slopes of lines. Write an equation of a line given information about the graph. Solve problems by writing equations. Writing an Equation of a Line. Slope-intercept form Given the slope m and the y-intercept b, y = mx + b Point-slope form

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3-4 Equations of Lines

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  1. 3-4 Equations of Lines You found the slopes of lines. • Write an equation of a line given information about the graph. • Solve problems by writing equations.

  2. Writing an Equation of a Line Slope-intercept form Given the slope m and the y-intercept b, y = mx + b Point-slope form Given the slope m and a point (x1,y1) y − y1 = m(x−x1) Two points Given two points (x1,y1) and (x2,y2)

  3. Page 198

  4. Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line. y = mx + b Slope-intercept form y = 6x + (–3) m = 6, b = –3 y = 6x – 3 Simplify.

  5. Use the slope of 6 or to findanother point 6 units up and1 unit right of the y-intercept. Answer: Plot a point at the y-intercept, –3. Draw a line through these two points.

  6. Write an equation in point-slope form of the linewhose slope is that contains (–10, 8). Then graph the line. Slope and a Point on the Line Point-slope form Simplify.

  7. Use the slopeto find another point 3 units down and 5 units to the right. Graph the given point (–10, 8). Draw a line through these two points.

  8. Two Points A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Step 1 First, find the slope of the line. Slope formula x1 = 4, x2 = –2, y1 = 9, y2 = 0 Simplify.

  9. Using (4, 9): Point-slope form Answer: Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Add 9 to each side.

  10. Two Points B.Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3). Step 1 First, find the slope of the line. Slope formula x1 = –3, x2 = –1, y1 = –7, y2 = 3 Simplify.

  11. Using (–1, 3): Point-slope form y = 5x + 8 Add 3 to each side. Answer: Step 2 Now use the point-slope form and either point to write an equation. m = 5, (x1, y1) = (–1, 3) Distributive Property

  12. Answer: Subtract 2 from each side. y = –2 Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form. Slope formula Step 1 This is a horizontal line. Step 2 Point-Slope form m = 0, (x1, y1) = (5, –2) Simplify.

  13. Page 200

  14. Parallel lines that are not vertical have equal slopes. • Two non-vertical lines are perpendicular if the product of their slope is -1. • Vertical and horizontal lines are always perpendicular to one another.

  15. Write Equations of Parallel or Perpendicular Lines y = mx + b Slope-Intercept form 0 = –5(2) + bm = –5, (x, y) = (2, 0) 0 = –10 + b Simplify. 10 = b Add 10 to each side. Answer:So, the equation is y = –5x + 10.

  16. RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. A. Write an equation to represent the total first year’s cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. A= mr+b Slope-intercept form A= 525r + 750 m = 525, b = 750 Answer: The total annual cost can be represented by the equation A = 525r + 750.

  17. RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. B. Compare this rental cost to a complex which charges a $200 annual maintenance fee but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate? Evaluate each equation for r = 12. First complex:Second complex: A= 525r + 750 A = 600r + 200 = 525(12) + 750 r = 12 = 600(12) + 200 = 7050 Simplify. = 7400 Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

  18. 3-4 Assignment Page 202, 13-39 odd

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