5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest...
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Transcript of 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest...
![Page 1: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/1.jpg)
5.3 Slope Intercept Form:
Linear Parent Function: is y = x or f(x) = x.
Parent Graph: Simplest function of a family of functions with common characteristics.
Linear Equation: is an equation that models a linear function.
Y-intercept: The point where the graph crosses the y-axis.
![Page 2: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/2.jpg)
GOAL:
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Whenever we are given a graph we must be able to provide the equation of the function.
Slope-Intercept Form: The linear equation of a nonvertical line:
Slope = =
y = m x + b
y-intercepty crossing
![Page 4: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/4.jpg)
EX: Provide the equation of the line in slope-intercept form.?
![Page 5: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/5.jpg)
Solution:The equation must be in slope-intercept form, that is in Y = mx + b1. Find the y-intercept (b) In this graph b = + 5.
2. Find another point to get the slope.
A(0,5)
B(3,8)
A(0,5) B(3,8)
![Page 6: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/6.jpg)
Use the equation of slope to find the slope:
= = = 1
The slope-intercept form equation is:
y = 1x + 5
A(0,5)
B(3,8)
Remember:This means that if you start a 5 and move up one and over to the right one, and continue this pattern, you can get many points ON this line.
![Page 7: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/7.jpg)
When work does not need to be shown: (EOC Test)
A(0,5)
B(3,8)
look at the triangle made by the two points.Count the number of square going up or down and to the right.In this case 3 up and 3 right. Thus slope is 3/3 = 1
![Page 8: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/8.jpg)
YOU TRY IT: Provide the equation of the line in
slope-intercept form.
![Page 9: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/9.jpg)
YOU TRY IT: (Solution)The equation must be in slope-intercept form, that is in Y = mx + b
1. Find the y-intercept (b)
In this graph b = + 4.
2. Find another point to get the slope. A(0,4) B(2,0)
A(0,4)
B(2,0)
![Page 10: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/10.jpg)
Use the equation of slope to find the slope:
= = = - 2
The slope-intercept form equation is:
y = -2x + 4Remember:This means that if you start a 4 and move down two and over to the right one, and continue this pattern, you can get many points ON this line.
A(0,4)
B(2,0)
![Page 11: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/11.jpg)
When no work is required, you can use the rise/run of a right triangle between the two points:
Look at the triangle, down 4 (-4) over to the right 2 (+2) slope = -4/+2 = -2
A(0,4)
B(2,0)
Remember:You MUST KNOW BOTH procedures, the slope formula and the triangle.
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Given Two Points: We can also create an equation in the slope-intercept form from any two points:
EX: Write the slope-intercept form of the line that passes through the points
(3, -2) and(1, -3)
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Use the given points and equation of slope:
= = = -
We now use the slope and a point to find the y intercept (b).
A(3,-2) B(1,-3)
y = mx + b -3 = - + b
Isolate b: -3 + = b
b = - + = -
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Going back to the equation:
y = mx + b
m = - and b = -
To get the final slope-intercept form of the line passing through (3, -2) and(1, -3)
we replace what we have found:
y = - x -
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We now proceed to graph the equation:
y = - x - 𝑹𝒊𝒔𝒆𝑹𝒖𝒏
Y-intercepty crossing
- 5
2
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YOU TRY IT: Write the slope-intercept form of the line that passes through the points (-3, 4) and(2, -1)
![Page 17: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/17.jpg)
Use the given points and equation of slope:
= = = -
We now use the slope and a point to find the y intercept (b).
A(3,-2) B(1,-3)
y = mx + b -3 = - + b
Isolate b: -3 + = b
b = - + = -
![Page 18: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/18.jpg)
Going back to the equation:
y = mx + b
m = - and b = -
To get the final slope-intercept form of the line passing through (3, -2) and(1, -3)
we replace what we have found:
y = - x -
![Page 19: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/19.jpg)
We now proceed to graph the equation:
y = - x - 𝑹𝒊𝒔𝒆𝑹𝒖𝒏
Y-intercepty crossing
- 5
2
![Page 20: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/20.jpg)
VIDEOS: Graphs
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/equation-of-a-line/v/linear-equations-in-slope-intercept-form
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/equation-of-a-line/v/slope-intercept-form-from-table
![Page 21: 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics.](https://reader036.fdocuments.in/reader036/viewer/2022062309/56649d0e5503460f949e4154/html5/thumbnails/21.jpg)
CLASSWORK:
Page 309-310
Problems: As many as needed to master the concept