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5.2 Equations of Lines Given the Slope and a Point

5.2 Equations of Lines Given the Slope and a Point. Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F-IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations. Today you will….

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5.2 Equations of Lines Given the Slope and a Point

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  1. 5.2 Equations of Lines Given the Slope and a Point

  2. Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F-IF.C.7, HS.F-LE.A.2):The student will understand that linear relationships can be described using multiple representations.

  3. Today you will… Find the equation of a line when you are given the slope of the line and any point on the line.

  4. Steps to write the equation in y = mx + b form given the slope and one point. • Write the equation y = mx + b • Plug the given slope into the m spot • Plug in the x and y values of the given point into the equation • Solve for b • Plug the solution into the equation for the b value.

  5. Write an equation of the line that passes through thepoint (6,-3)with aslope of -2. Follow the steps: y = mx + b -3 = -2(6) + b(plug in m, x, and y) -3 = -12 + b (add 12 to both sides) 9 = b y=-2x+9(plug in the m and b value)

  6. Graphic Check: y = -2x + 9 Note that the line crosses the y-axis at the point (0,9) and passes through the given point (6,-3). Use real graph paper and plug in (0,9) on the y-axis. Count down 2 back one until you cross (6,-3).

  7. Find the equation of a line with a slope of 4 and a point of (8, 3) on the line. Follow the steps: y = mx + b 3 = 4(8) + b(plug in m, x, and y) 3 = 32 + b (subtract 32 from both sides) -29 = b y= 4x - 29(plug in the m and b value)

  8. Real-life application • Between 1980 and 1990 the number of vacations taken by Americans increased by about 15,000,000 per year. • In 1985 Americans went on 340,000,000 vacation trips. • Find an equation that gives the number of vacation trips, y (in millions), in terms of years, t.

  9. Question What is your slope? What is your given point? Solution It is your rate of change. The constant rate is 15 million trips/year, so m= 15 (5, 340) Where 5 represents 1985 340 represents the number of trips in millions A Linear Model for Vacation Travel

  10. Now follow the steps and find the equation when m = 15 and the given point is (5, 340) Follow the steps: y = mx + b 340 = 15(5) + b(plug in m, x, and y) 340 = 75 + b (subtract 75 from both sides) 265 = b y= 15x + 265(plug in the m and b value) So the slope-intercept form of the equation is y=15t+265

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