2.2: Linear Equations. Graphing Linear Equations y is called the dependent variable because the...
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Transcript of 2.2: Linear Equations. Graphing Linear Equations y is called the dependent variable because the...
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2.2: Linear Equations
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Graphing Linear Equations• y is called the dependent variable because the value of y depends on x
• x is called the independent variable
4Ex1) Graph the equation 23
y x
y mx b
Will this be a function??
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Standard FormStandard form of a linear equation is Ax + By = C, where A, B, and C are real numbers and A, B ≠ 0.
Graph linear equations in standard form by finding the x- and y- intercepts
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Ex2) 2 4 8x y
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More PracticeEx3) The equation 3x + 2y = 120 models the number of passengers who can sit in a train car, where x is the number of adults and y is the number of children. Graph the equation. Explain what the x- and y- intercepts represent. Describe the domain and range.
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Point-Slope FormThe line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Ex6) Write in standard form an equation of the line with1slope through the point ( 6,2).3
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Point-Slope FormThe line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Ex7) Find the equation of a line through the points (-2, 3) and (1, 6). Then write it in standard form.
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Slope-Intercept Form
y = mx + bEx8) What is the slope of the line 4x + 6y = 18?
What is the slope of:
a horizontal line?
a vertical line?
parallel lines?
perpendicular lines?
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Perpendicular LinesEx9) Write an equation of the line through (5, –3) and perpendicular to y = 4x + 1. Graph both lines.
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Exit Problems:1. Determine the slope, and the x- and y- intercepts of each of
the functions2. Write the equation in both standard and y-intercept form3. Graph the equations
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Exit Problems:1. Determine the slope, and the x- and y- intercepts of each of
the functions2. Write the equation in both standard and y-intercept form3. Graph the equations
![Page 11: 2.2: Linear Equations. Graphing Linear Equations y is called the dependent variable because the value of y depends on x x is called the independent variable.](https://reader034.fdocuments.us/reader034/viewer/2022051301/5a4d1b117f8b9ab05998f63b/html5/thumbnails/11.jpg)
Exit Problems:1. Determine the slope, and the x- and y- intercepts of each of
the functions2. Write the equation in both standard and y-intercept form3. Graph the equations
![Page 12: 2.2: Linear Equations. Graphing Linear Equations y is called the dependent variable because the value of y depends on x x is called the independent variable.](https://reader034.fdocuments.us/reader034/viewer/2022051301/5a4d1b117f8b9ab05998f63b/html5/thumbnails/12.jpg)
Special Lines:
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Special Lines:
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2.2: Linear Equations
Our greatest glory is not in never falling, but in getting up every time we do.
Homework #10
Pg 67 # 2-14 even, 20 – 34 even, 37, 42, 54