warmup
DESCRIPTION
Warmup. Write the equation for each of the following: Slope (word form) Slope (equation form) Midpoint Distance (Store method or actual formula) Direct Variation Standard Form of a Line Remember, you need to MEMORIZE these!!! Expect a Quiz on exactly this SOON! STUDY!!!. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/1.jpg)
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!!!
![Page 2: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/2.jpg)
Essential Question
How does slope effect the graph of a line?
![Page 3: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/3.jpg)
How does a
Positive Slope
look?
![Page 4: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/4.jpg)
y = 1xy = x aka
![Page 5: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/5.jpg)
y = 2x
![Page 6: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/6.jpg)
y = 3x
![Page 7: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/7.jpg)
y = 4x
![Page 8: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/8.jpg)
y = 5x
![Page 9: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/9.jpg)
y = 6x
![Page 10: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/10.jpg)
y = 7x
![Page 11: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/11.jpg)
y = 8x
![Page 12: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/12.jpg)
y = 9x
![Page 13: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/13.jpg)
y = 20x
![Page 14: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/14.jpg)
y = 50x
![Page 15: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/15.jpg)
How does a
Fractional Slope
look? (or decimal)
![Page 16: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/16.jpg)
y = 1xy = x aka
![Page 17: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/17.jpg)
y=(1/2)x
![Page 18: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/18.jpg)
y=(1/3)x
![Page 19: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/19.jpg)
y=(1/4)x
![Page 20: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/20.jpg)
y=(1/5)x
![Page 21: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/21.jpg)
y=(1/6)x
![Page 22: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/22.jpg)
y=(1/7)x
![Page 23: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/23.jpg)
y=(1/8)x
![Page 24: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/24.jpg)
y=(1/9)x
![Page 25: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/25.jpg)
y=(1/20)x
![Page 26: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/26.jpg)
y=(1/50)x
![Page 27: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/27.jpg)
How does a
Negative Slope
look?
![Page 28: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/28.jpg)
y=1x vs y=-1x
![Page 29: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/29.jpg)
y=-1xy = -x aka
![Page 30: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/30.jpg)
y=-2x
![Page 31: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/31.jpg)
y=-3x
![Page 32: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/32.jpg)
y=-4x
![Page 33: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/33.jpg)
y=-5x
![Page 34: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/34.jpg)
How does a
Positive Y-Intercept
look?
![Page 35: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/35.jpg)
y = x + 0y=x aka
![Page 36: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/36.jpg)
y = x + 1
![Page 37: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/37.jpg)
y = x + 2
![Page 38: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/38.jpg)
y = x + 3
![Page 39: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/39.jpg)
y = x + 4
![Page 40: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/40.jpg)
y = x + 5
![Page 41: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/41.jpg)
y = x + 6
![Page 42: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/42.jpg)
y = x + 7
![Page 43: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/43.jpg)
y = x + 8
![Page 44: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/44.jpg)
y = x + 9
![Page 45: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/45.jpg)
How does a
Negative Y-Intercept
look?
![Page 46: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/46.jpg)
y=x aka y = x – 0 aka y=x+0
![Page 47: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/47.jpg)
y = x - 1
![Page 48: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/48.jpg)
y = x - 2
![Page 49: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/49.jpg)
y = x - 3
![Page 50: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/50.jpg)
y = x - 4
![Page 51: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/51.jpg)
y = x - 5
![Page 52: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/52.jpg)
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)
![Page 53: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/53.jpg)
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
![Page 54: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/54.jpg)
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…
![Page 55: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/55.jpg)
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…
![Page 56: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/56.jpg)
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
![Page 57: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/57.jpg)
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!
![Page 58: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/58.jpg)
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!)
![Page 59: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/59.jpg)
Remember!
Parallel Lines: Same Slope!
Perpendicular Lines: Slopes are Negative
Reciprocals!
![Page 60: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/60.jpg)
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…
![Page 61: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/61.jpg)
First you must find 1. __________ 2. __________
On Turn in Sheet…
slope
Y-intercept
![Page 62: Warmup](https://reader035.vdocuments.us/reader035/viewer/2022062501/568161e6550346895dd20c6f/html5/thumbnails/62.jpg)
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…