Download - Warmup
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…