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Graphs & Linear Equations Y X

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Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y always equals 4)

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Graphing Horizontal & Vertical Lines Y X This line has a x value of 1 for any y-value. Its equation is x = 1 (meaning x always equals 1)

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The Equation of a Vertical Line is X=Constant Y X x = 1

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The Equation of a Horizontal Line is Y=Constant Y X y = 3

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Graph the following lines Y = -4 Y = 2 X = 5 X = -5 X = 0 Y = 0

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Answers Y X x = 5 x = -5

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Answers Y X y = -4 y = 2

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Answers Y X x = 0 y = 0

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SLOPE = Slope is a measure of STEEPNESS

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The Symbol for SLOPE = m Think of m for Mountain

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SLOPE = How much does this line rise? How much does it run? (3,2) (6,4) (0,0) 1 2 3 1 2 4 3 56 4

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SLOPE = How much does this line rise? How much does it run? (3,2) (6,4) (0,0) 1 2 3 1 2 4 3 56 4

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m=SLOPE = (3,2) (6,4) (0,0) 1 2 3 1 2 4 3 56 4 x1y1x1y1 x2y2x2y2

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(x 2,y 2 ) (64) (x 1,y 1 ) (3,2) Switch points and calculate slope Make (3,2) (x 2,y 2 ) & (6,4) (x 1,y 1 ) (x 1,y 1 ) (6,4) (x 2,y 2 ) (3,2)

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Recalculation with points switched (x 1,y 1 ) (6,4) (x 2,y 2 ) (3,2) Same slope as before

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It doesnt matter what 2 points you choose on a line the slope must come out the same

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Keeping Track of Signs When Finding The Slope Between 2 Points Be Neat & Careful Use (PARENTHASES) Double Check Your Work as you Go Follow 3 Steps

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3 Steps for finding the Slope of a line between 2 Points (3,4)&(-2,6) 1st Step: Write x 1,y 1,x 2,y 2 over numbers 2nd Step: Write Formula and Substitute x 1,x 2,y 1,y 2 values. 3rd Step: Calculate & Simplify (3,4) & (-2,6) x 1 y 1 x 2 y 2

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Find the Slopes of Lines containing these 2 Points 1. (1,7) & (5,2) 5. (3,6) & (5,-5) 3. (-3,-1) & (-5,-9) 6. (1,-4) & (5,9) 4. (4,-2) & (-5,4) 2. (3,5) & (-2,-8)

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1. (1,7) & (5,2) 5. (3,6) & (5,-5) 3. (-3,-1) & (-5,-9) 6. (1,-4) & (5,9) 4. (4,-2) & (-5,4) 2. (3,5) & (-2,-8) ANSWERS

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Solve for y if (9,y) & (-6,3) & m=2/3

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Review Finding the Slopes of Lines Given 2 Points 1st Step: Write x 1,x 2,y 1,y 2 over numbers 2nd Step: Write Formula and Substitute x 1,x 2,y 1,y 2 values. 3rd Step: Calculate & Simplify NOTE: Be Neat, Careful, and Precise and Check your work as you go..

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ZERO Slope Horizontal Positive Slope Is Up the Hill Negative Slope Is Down the Hill NO Slope Vertical Drop

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ZERO Slope Horizontal NO Slope Vertical Drop

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Parallel Lines Have the Same Slope (0,0) 1 2 3 1 2 4 3 56 4 5

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Perpendicular Lines Have Neg. Reciprocal Slopes (0,0) 1 2 3 1 2 4 3 56

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