Warmup• Write the equation for each of the following:

1. Slope (word form)2. Slope (equation form)3. Midpoint4. Distance (Store method or actual formula)5. Direct Variation6. Standard Form of a Line

Remember, you need to MEMORIZE these!!!Expect a Quiz on exactly this SOON! STUDY!!!

Essential Question

How does slope effect the graph of a line?

How does a

Positive Slope

look?

y = 1xy = x aka

y = 2x

y = 3x

y = 4x

y = 5x

y = 6x

y = 7x

y = 8x

y = 9x

y = 20x

y = 50x

How does a

Fractional Slope

look? (or decimal)

y = 1xy = x aka

y=(1/2)x

y=(1/3)x

y=(1/4)x

y=(1/5)x

y=(1/6)x

y=(1/7)x

y=(1/8)x

y=(1/9)x

y=(1/20)x

y=(1/50)x

How does a

Negative Slope

look?

y=1x vs y=-1x

y=-1xy = -x aka

y=-2x

y=-3x

y=-4x

y=-5x

How does a

Positive Y-Intercept

look?

y = x + 0y=x aka

y = x + 1

y = x + 2

y = x + 3

y = x + 4

y = x + 5

y = x + 6

y = x + 7

y = x + 8

y = x + 9

How does a

Negative Y-Intercept

look?

y=x aka y = x – 0 aka y=x+0

y = x - 1

y = x - 2

y = x - 3

y = x - 4

y = x - 5

In Summary…Standard Form of a Line: y = mx + b 1. m is the slope

- (How steep the line is)- bigger slope means steeper line- can be positive (uphill) or negative

(downhill)

2. b is the y-intercept- (where the line crosses the y-axis)

Where does each of the following cross the y-axis? Which line is the steepest?

1. y=2x+7 2. y=-x+11 3. y=1/2x-8

Where does each line cross the y-axis and which is steepest?

1. y=x+8 2. y=3x-4 3. y=1/3x+3 4. y=-x+5 5. y=-2x+5 6. y=-1/3x

On Turn in Sheet…

Write a linear equation for each: y=mx+b

1. m=5, b=-32. m=1/2, b=73. m=3, b=-34. m=5, b=1/35. m=7, b=2/36. m=0, b=-4 This is called

________7. m=2, b=0

On Turn in Sheet…

Drawing Conclusions…Look at the 3 lines to the right. Each line has the same _____

Graph the 3 lines in your calculator. Look at the lines. What can you conclude?

Lines with the same ______ are ______

slope parallel

slope

Drawing Conclusions…What if you wanted to find a line Perpendicular to a given line? Would such a line have the same slope as the original line?

Perpendicular lines have slopes that are negative reciprocals. That means change the sign, and flip the fraction!

Note that they don’t look perfectly perpendicular on your calculator screen. This is because your screen is stretched more left and right than it is up and down! (It’s not Square!)

Remember!

Parallel Lines: Same Slope!

Perpendicular Lines: Slopes are Negative

Reciprocals!

Write the equation of a line (a) parallel to each of the following: (b) perpendicular to each of the following:

1.y=3x-4 a.______ b.______2. y=1/3x+3 a.______ b.______3. y=-x+5 4. y=-2x+5 5. y=-1/3x6. y=x+8

On Turn in Sheet…

First you must find 1. __________ 2. __________

On Turn in Sheet…

slope

Y-intercept

Graph the following linear equations:

1. y=x+8 2. y=3x-4 3. y=1/3x+3 4. y=-x+5 5. y=-2x+5 6. y=-1/3x

On Turn in Sheet…