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Copy the following into your notes

Copy the following into your notes. Direct Variation y = k x k = Constant of Variation Same as Slope 1. When given Y and X, solve for K 2. Then use K to solve for missing variable Y = KX goes through Origin Use K as slope to graph line (Up then over to find second point).

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Copy the following into your notes

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  1. Copy the following into your notes Direct Variation y = kx k= Constant of Variation Same as Slope 1. When given Y and X, solve for K 2. Then use K to solve for missing variable Y = KX goes through Origin Use K as slope to graph line (Up then over to find second point) Slope Intercept y = mx + b m = slope b = y intercept When graphing using slope intercept. • Find Y intercept • Use slope to find second point • Remember if the slope is not a fraction, a whole number is over 1. • Slope • + (Positive) Slope Increasing • (Negative) Slope – Decreasing • 0 Slope – Horizontal • #/0 – Undefined – Vertical • Higher the Slope, Steeper Line • Lower Slope, Flatter the Line Y2 –Y1 rise m= M=2 m= run X2 –X1 M=1 M=1/2 Run Rise Y intercept

  2. 4.2Writing Equations in Slope Intercept Form CFU3102.3.21 Determine the equation of a line using given information including a point and slope, two points, a point and a line parallel or perpendicular, graph, intercepts. SPI 3102.1.2Write an equation symbolically to express a contextual problem.; SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

  3. 4.2 Writing Equations in Slope Intercept Form In 1995, the population of Orlando was about 175,000 growing at a rate of 2000 per year. Assuming the growth rate remains constant can you calculate the population for the year 2001? What is the slope? M = 2000 What else do you know? Y = 175,000 and X = 1995 What is the population in 1997 175,000 + 2(2000) 179,000 CFU 3102.3.23 Determine the graph of a linear equation including those that depict contextual situations

  4. Given Slope and One Point • Write and equation of a line with slope =2 passing through the point (1,5) Y = MX + B 5 = 2(1)+ B 5 = 2+ B -2 -2 3 = B Y =2X + 3 Y=MX + B

  5. Given Slope and One Point • Write and equation of a line with slope =1/2 • passing through the point (2,-3) Y = MX + B -3 = 1/2(2)+ B -3 = 1+ B -1 -1 -4 = B Y =1/2X -4 Y=MX + B

  6. Given two points • Write and equation of line that passes through the following ordered pairs • (-3, -1) and (6, -4) Y = MX + B -1 = -1/3(-3)+ B Y2 –Y1 Y2 –Y1 -3 -4 –(-1) -1 -4 +1 m= m= m= m= m= m= 6 +3 X2 –X1 3 9 X2 –X1 6-(-3) -1 = +1+ B -1 -1 -2 = B Y = -1/3X - 2 Y=MX + B

  7. Given two points • Write and equation of line that passes through the following ordered pairs • (-3, -4) and (-2, -8) Y = MX + B -8 = -4(-2)+ B -4 -8 –(-4) -8 +4 Y2 –Y1 Y2 –Y1 m= m= -4 m= m= m= m= -2 +3 -2-(-3) X2 –X1 1 X2 –X1 -8 = 8 + B -8 -8 -16= B Y = -4X -16 Y=MX + B

  8. Summary • Slope and One Point • Substitute the values of m, x, and y into slope-intercept form and solve for b. • Write the slope-intercept form using m and b. Y2 –Y1 Two Points • Calculate the Slope • Choose one of the points to use, then • Substitute the values of m, x, and y into slope-intercept form and solve for b. • Write the slope-intercept form using m and b. m= X2 –X1 Y=MX + B

  9. Practice Assignment • Page 227, 10 - 24 E, 31 - 33 All

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