Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors...
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![Page 1: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/1.jpg)
Graphing Linear Equations, Point-Slope Form, and
Parallel/Perpendicular linesREVIEW
Algebra HonorsMr Smith
![Page 2: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/2.jpg)
Objective
• By the end of this lesson you should be able to take given points or slope and graph and write it in point-slope, slope-intercept, and standard forms.
• By the end of this lesson you should be able to write equations for parallel and perpendicular lines.
![Page 3: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/3.jpg)
Slope- Intercept form
• To _______, it is best to have the linear equation in slope-intercept form.
• Slope intercept form is y = ___ + ___• The 4 variables and definitions of slope int
form are:___ = _______ ____ = ___________ = _______ ____ = ________Pause!
![Page 4: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/4.jpg)
Slope- Intercept form
• To _Graph_, it is best to have the linear equation in slope-intercept form.
• Slope intercept form is y = mx + b• The 4 variables and definitions of slope int
form are:_y_ = total _m_ = slope_ x = units_ b = y - intercept
![Page 5: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/5.jpg)
Writing in slope- intercept
• Slope = 5, y-int = -7
• 4x + 3y = 18 (-4, 6) (3, -8)
Pause!
![Page 6: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/6.jpg)
Writing and Graphing in slope- intercept form
1. Slope = 5, y-int = -7 y = 5x - 72. 4x + 3y = 18 3. (-4, 6) (3, -8)= -4x -4x m = = -2
3y = -4x + 18 y=mx+b 3 3 6=-2(-4)+b
y = 6=8+bb = -2 y=-2x-2
![Page 7: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/7.jpg)
Graphing
For the following, the first slide is the problem, the second is the solution
The first step, which we just did, is to put the info into slope-int form, and then graph.
![Page 8: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/8.jpg)
Now, Graph y = 5x - 7
![Page 9: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/9.jpg)
Graph y = 5x - 7
![Page 10: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/10.jpg)
Graph y =
![Page 11: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/11.jpg)
Graph y =
![Page 12: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/12.jpg)
Graph y=-2x-2
![Page 13: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/13.jpg)
Now, Graph y=-2x-2
![Page 14: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/14.jpg)
Point-Slope Form
• You can write the equation of a line using point slope form, even if you do not know the second point on a line.
![Page 15: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/15.jpg)
Write in point-slopey – y1 = m (x – x1)
A line passing through point (4, -5) with a slope of -2
Pause!
![Page 16: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/16.jpg)
Write in point-slopey – y1 = m (x – x1)
A line passing through point (4, -5) with a slope of -2y + 5 = -2 (x – 4)
Next, write this in slope- int, and then standard form
Pause!
![Page 17: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/17.jpg)
To slope – int To standard
y + 5 = -2 (x – 4) y = -2x + 3y + 5 = -2x + 8 +2x +2x -5 -5 2x + y = 3 y = -2x + 3
![Page 18: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/18.jpg)
Write in point-slopey – y1 = m (x – x1)
A line passing through (3, -4) and (-6, -1)
Pause!
![Page 19: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/19.jpg)
Write in point-slopey – y1 = m (x – x1)
A line passing through (3, -4) and (-6, -1)1. Find the slope = =
next, put into slope-int and standard
2. Pick a point and the slope y - -4 = (x – 3) y + 4 = (x – 3)
Pause!
![Page 20: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/20.jpg)
To slope – int To standard
y + 4 = (x – 3) y = x + 3 + x +
y + 4 = x + 1 (3) x + y = 3(3) -4 -4 y = x + 3 x + 3y = 9
![Page 21: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/21.jpg)
Parallel and Perpendicular
Parallel lines Have the same slope, but different y-intercepts
Perpendicular Lines have Opposite Reciprocal slopes, but could have the same intercept.
Example: a slope of has opposite reciprocal slope of -
![Page 22: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/22.jpg)
Write the equation of a line that is…
Parallel to y = 5x + 6, and goes through (-5, 9)Slope is the same, so m=5, solve for b:y = mx+b > 9 = 5(-5) + b 9 = -25 + b
+25 +25 34 = b, so …
y = 5x + 34 is the answer
![Page 23: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/23.jpg)
Write the equation of a line that is…
Perpendicular to y=5x+6, and goes through(-3,6)Slope is opposite reciprocal, so m = - y = mx + b > 6 = - (-3) + b > 6 = + b
- - 5 = b, so… y = - + 5
Yes, you can have intercepts that are not integers
![Page 24: Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.](https://reader035.fdocuments.net/reader035/viewer/2022070413/5697bfc61a28abf838ca74cd/html5/thumbnails/24.jpg)
Things to Remember
• To Graph, you should use slope-intercept form. Start at the y-intercept, and then plot the slope from there.
• Moving between forms really comes down to moving terms around, and watching your signs.
• Parallel lines have the same slope, perpendicular lines are opposite reciprocals.