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**Graphs & Linear Equations**

Y y=mx+b X

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**Graphing Horizontal & Vertical Lines**

This line has a y value of 4 for any x-value. It’s equation is y = 4 (meaning y always equals 4) Y y-axis X x-axis

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**Graphing Horizontal & Vertical Lines**

This line has a x value of 1 for any y-value. It’s equation is x = 1 (meaning x always equals 1) Y y-axis X x-axis

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**The Equation of a Vertical Line is X=Constant**

Y y-axis x = 1 X x-axis

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**The Equation of a Horizontal Line is Y=Constant**

y-axis y = 3 X x-axis

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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 x = -5 x = 5 Y y-axis X x-axis

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Answers Y y-axis y = 2 X x-axis y = -4

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Answers Y y-axis y = 0 X x-axis x = 0

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SLOPE = NEGATIVE-DOWN POSITIVE-UP Slope is a measure of STEEPNESS

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**Think of m for Mountain The Symbol for SLOPE = m NEG. Slope is -m**

POS. Slope is +m Think of m for Mountain

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**SLOPE = How much does this line rise? How much does it run? (6,4) 4 •**

3 (3,2) 2 • 1 (0,0) 1 2 3 4 5 6 How much does this line rise? How much does it run?

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**SLOPE = 2 3 2 3 How much does this line rise? How much does it run?**

(6,4) 4 • 3 (3,2) 2 • 1 (0,0) 1 2 3 4 5 6 How much does this line rise? How much does it run? 2 3

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m=SLOPE = x2y2 (6,4) 4 • x1y1 3 (3,2) 2 • 1 (0,0) 1 2 3 4 5 6

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**Switch points and calculate slope Make (3,2) (x2,y2) & (6,4) (x1,y1)**

• • (x1,y1)(3,2) (x2,y2)(3,2) • •

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**Recalculation with points switched**

(x1,y1)(6,4) • (x2,y2)(3,2) • Same slope as before

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**It doesn’t 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 x1,y1,x2,y2 over numbers 2nd Step: Write Formula and Substitute x1,x2,y1,y2 values. 3rd Step: Calculate & Simplify x1 y1 x2 y2 (3,4) & (-2,6)

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**Find the Slopes of Lines containing these 2 Points**

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

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

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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 x1,x2,y1,y2 over numbers 2nd Step: Write Formula and Substitute x1,x2,y1,y2 values. 3rd Step: Calculate & Simplify NOTE: Be Neat, Careful, and Precise and Check your work as you go..

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

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NO Slope Vertical Drop ZERO Slope Horizontal

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**Parallel Lines Have the Same Slope**

5 4 • 3 2 • 1 (0,0) 1 2 3 4 5 6

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**Perpendicular Lines Have Neg. Reciprocal Slopes**

3 2 1 (0,0) 1 2 3 4 5 6

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1.4 Linear Equations in Two Variables

1.4 Linear Equations in Two Variables

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