Linear Equations Review Geometry Prerequisite: GA1c1: I can write a linear equation in standard form...
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Transcript of Linear Equations Review Geometry Prerequisite: GA1c1: I can write a linear equation in standard form...
Linear Equations ReviewLinear Equations ReviewGeometry Prerequisite:GA1c1: I can write a linear equation in standard form given two points.GA1c2: I can write a linear equation in slope intercept form given two points.GA1c3: I can write a linear equation in standard form given a point and the slope.GA1c4: I can write a linear equation in slope intercept form given a point and the slope.GA1c5: I can write a linear equation in standard form given the graph of the equation.GA1c6: I can write a linear equation in slope intercept form given the graph of the equation.
GA1d1: I can recognize the concept of slope as a rate of change.GA1d2: I can determine the slope given the equation of a line in standard form.GA1d3: I can determine the slope given the equation of a line in slope intercept form.GA1d4: I can determine the slope given the graph of a line.GA1d5: I can determine the slope given the two points on a line.GA1d6: I can determine the slope given a verbal description of a line.
GA1e1: I can graph a linear equation using a table of values.GA1e2: I can graph a linear equation using x- and y- intercepts.GA1e3: I can graph a linear equation using the slope and intercept.
What you should know aboutWhat you should know aboutLinear equationsLinear equations
Slopey-interceptx-interceptWhat does the graph look
like?Parallel slopePerpendicular slope
Given ANY linear equation you should be able to identify…
Equation FormsEquation Forms
Slope Intercept
StandardHorizontalVertical
y = mx + bAx + By = Cy = bx = a
SlopesSlopesNegativePositive
Horizontal Vertical
Can you run through the Can you run through the linear equation information…linear equation information…
3x+4y=243x+4y=24
y = 1/2x-7y = 1/2x-7
y = 5y = 5
x = 6x = 6
Given any linear equation, one Given any linear equation, one should be able to should be able to 3x+4y=243x+4y=24
The Equation FormDirectionSlopey-interceptx-interceptParallel SlopePerpendicular Slope
1. Standard2. Falling gently3. -3/4 4. 65. 86. -3/4 7. 4/3
identify…
Given any linear equation, one Given any linear equation, one should be able to should be able to y = 1/2x-7y = 1/2x-7
The Equation FormDirectionSlopey-interceptx-interceptParallel SlopePerpendicular Slope
1. Slope intercept2. Rising, gently3. 1/24. -75. -(-7)/(1/2) = 146. 1/27. -2
identify…
Given any linear equation, one Given any linear equation, one should be able to should be able to y = 5y = 5
The Equation FormDirectionSlopey-interceptx-interceptParallel SlopePerpendicular Slope
1. Horizontal line2. horizontal3. 04. 55. Does not exist6. 07. undefined
identify…
Given any linear equation, one Given any linear equation, one should be able to should be able to x x = 6 = 6
The Equation FormDirectionSlopey-interceptx-interceptParallel SlopePerpendicular Slope
1. Vertical line2. verticle3. undefined 4. Does not exist5. 66. undefined 7. 0
identify…
To graph a lineTo graph a line
Intercepts◦Identify the intercepts
◦Plot the intercepts
◦Draw the line
Point-slope◦Identify a point on the line and the slope
◦Plot the point◦Count the slope “Rise/Run”
(0,-7)
(-7/3,0)
Graph using intercepts Graph using intercepts y = -y = -3x – 73x – 7
y-int = -7
x-int = 7
-3
up 3 back 1
(0,-7)
down 3 over 1
Graph using intercepts Graph using intercepts y = -y = -3x – 73x – 7
point= (0, -7)
slope = -3 / 1
The slope formulaThe slope formula
m = y1 – y2
x1 – x2
This is really the same at the point-slope equation
m(x1 – x2) = y1 – y2
y1 – y2 = m(x1 – x2)
Find the slope given 2 points (-Find the slope given 2 points (-1,1); (2,3)1,1); (2,3)
m = 3 – 1 2 – -1m = 2 3
m = 1 – 3 -1 – 2m = -2 = 2 -3 3
Now write the equation (-1,1); Now write the equation (-1,1); (2,3)(2,3)
m = 3 – 1 2 – -1
m = 2 3
y1 – y2 = m(x1 – x2)y – 3 = 2/3 (x – 2)y = 2/3 x – 4/3 + 9/3y = 2/3 x + 5/3
If you have two points you can find If you have two points you can find the line…sometimes the challenge is the line…sometimes the challenge is knowing what you have.knowing what you have.
Given◦ The origin◦ The y-intercept◦ The x-intercept◦ A line parallel to
the x-axis◦ A line parallel to
the y-axis
You have …◦ the point (0,0)◦ the point (0,y)◦ the point (x,0)◦ the slope m = 0 eqn is y = ____◦ The slope m
undefined eqn is x = ____
Parallel & PerpendicularParallel & Perpendicular II II | |
Parallel slopes are equal
m original
m|| = mo
Perpendicular slopes are opposite reciprocals
m original
m | = -1 / mo
Linear equation partsLinear equation partsSlope
InterceptStandard Horizontal Vertical
Equationy = mx +
bAx + By =
C y = b x = a
Slope m-A
B0 undefined
y – intercept
bC
Bb
does not exist
x - intercept
-b m
C A
does not exist
a
parallel slope ||
m-A
B0 undefined
perpendicular slope _|_
-1 m
B A
undefined 0
Given 3x + 4y = 12Given 3x + 4y = 12Find the line || to
the given line that passes through (-2, 5).
Find the line _|_ to the given line that passes through (-2, 5).
Given 3x + 4y = 12Given 3x + 4y = 12Find the line || to
the given line that passes through (-2, 5).
Find the line _|_ to the given line that passes through (-2, 5).
If the line is parallel then the slope must be the same so the linear
equation will look like 3x + 4y =
If the line is perpendicular then the slope must be the opposite
reciprocal so the linear equation will look like -4x + 3y =
Given 3x + 4y = 12Given 3x + 4y = 12Find the line || to
the given line that passes through (-2, 5).
3x + 4y = ___3(-2) + 4(5) = ___-6 + 20 = 14
Find the line _|_ to the given line that passes through (-2, 5).
-4x + 3y = ___-4(-2)+3(5) = ___8+15 = 23
3x + 4y = 143x + 4y = 14 -4x + 3y = 23-4x + 3y = 23
Given y = 2x - 12Given y = 2x - 12Find the line || to
the given line that passes through (-2, 5).
Slope = 2 thereforem|| = 2
Find the line _|_ to the given line that passes through (-2, 5).
Slope = 2 thereforem_|_ = -1/2
y = 2x + by = 2x + b y = -1/2 x + by = -1/2 x + b
Given y = 2x - 12Given y = 2x - 12Find the line || to
the given line that passes through (-2, 5).
Find the line _|_ to the given line that passes through (-2, 5).
y = 2x + by = 2x + b5 = 2(-2) + b5 = 2(-2) + bb = 9b = 9
y = -1/2 x + by = -1/2 x + b5 = -1/2 (-2) + 5 = -1/2 (-2) + bbb = 4b = 4
y = -1/2 x + 4y = -1/2 x + 4y = 2x + 9y = 2x + 9
The alternative calculation is The alternative calculation is to using the point slope form to using the point slope form of a linear equation y – yof a linear equation y – y11 = = m(x – xm(x – x11))Once you identify
the desired slope, you have m
then you can substitute the point value for (x1,y1)
y = -3x – 7y = -3x – 7parallel through
(1,2)
perpendicular through (1,2)
y – 2 = -3(x – 1) y – 2 = 1/3(x – 1)
Find (e,f)Find (e,f)
remember if you can find the remember if you can find the equation of the blue lineequation of the blue line
you can find the y - you can find the y - interceptinterceptthen consider the then consider the reflectionreflection
Find tFind t
Select t so that the triangle with vertices ( -4, 2 ), ( 5, 1 ), and (t,-1) a right triangle with the right angle at (t,-1).
Find tFind t
Select t so that the triangle with vertices ( -4, 2 ), ( 5, 1 ), and (t,-1) a right triangle with the right angle at (t,-1).
Right angle
Now go practice…Now go practice…