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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Standard Form Standard 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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Page 1: 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

2.2: Linear Equations

Page 2: 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

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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??

Page 3: 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

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

Page 4: 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

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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.

Page 5: 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

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

Page 6: 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

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.

Page 7: 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

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?

Page 8: 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

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Perpendicular LinesEx9) Write an equation of the line through (5, –3) and perpendicular to y = 4x + 1. Graph both lines.

Page 9: 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

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 10: 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

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

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

Special Lines:

Page 13: 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

Special Lines:

Page 14: 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

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