Graphs & Linear Equations Y y=mx+b X

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

It doesn’t matter what 2 points you choose on a line the slope must come out the same

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

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)

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)

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)

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

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..

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

NO Slope Vertical Drop ZERO Slope Horizontal

Parallel Lines Have the Same Slope 5 4 • 3 2 • 1 (0,0) 1 2 3 4 5 6

Perpendicular Lines Have Neg. Reciprocal Slopes 3 2 1 (0,0) 1 2 3 4 5 6