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**The equation of a line - Equation of a line - Slope - Y intercept**

y = mx + b - Equation of a line - Slope - Y intercept -when given slope and y intercept -when given slope and a point -when given two ordered pairs

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**Equation of a line y m x b y = m*x + b**

Y coordinate of a point on the line X coordinate of a point on the line Slope of the line Y intercept, the point on the y axis that the line passes through m x b

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**Slope Calculating Slope y = m*x + b Slope is represented by m**

Slope is Rise/Run When given two points, (x1,y1), (x2,y2) m = (y2-y1)/(x2-x1) Example

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**Slope Calculating Slope y = m*x + b Slope is represented by m**

Slope is Rise/Run When given an ordered pair, (x,y), and y intercept, b, Substitute x Substitute y Substitute b Solve for m Example

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**Calculating y intercept**

y = mx + b Y intercept is represented by b When given m and an ordered pair, (x,y), plug in y,x, and m and solve for b Example

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**Finding y intercept Given : (1,2) m = 3 Equation of a line :**

y = mx + b y = 3x + b y = 3(1) + b 2 = 3(1) + b 2 = 3 + b 2 – 3 = 3 + b – 3 -1 = b The y intercept is -1

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**Equation of a Line (when given a slope and y intercept )**

Given : m = 2 , b = 3 The equation of a line is y = mx + b -Substitute m -y = 2x + b -Substitute b -y = 2x + 3

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**Equation of a Line (when given two ordered pairs)**

Calculate slope m = 1 Calculate y intercept b = 1 Substitute m and b into y = mx + b y = 1x + 1

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**Finding Slope (given 2 points) Given : (x1, y1), (x2, y2)**

m = (y2 – y1)/(x2-x1) Substitute y2 Substitute y1 Subtract (y2-y1) Substitute x2 Substitute x1 Subtract (x2-x1) Divide (y2-y1)/(x2-x1)

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Equation Finding (when given 2 points) Given (x1,y1), (x2,y2) Calculate slope Substitute an ordered pair (x,y) Substitute m Solve for b y = mx + b For the final answer leave the y and x but substitute the m and b

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**(Calculating slope when given ordered pair and y intercept)**

Equations (Calculating slope when given ordered pair and y intercept) Given : (x1,y1) :(1,2), b = 1 Substitute y1 in for y (2 = mx + b) Substitute x1 in for x (2 = m(1) + b) Substitute b in for b (2 = m(1) + 1) Solve for m 2-1 = m +1 – 1 m = 1

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2.2 Linear Equations.

2.2 Linear Equations.

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