2.2: Linear Equations Our greatest glory is not in never falling, but in getting up every time we do.

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Presentation transcript:

2.2: Linear Equations Our greatest glory is not in never falling, but in getting up every time we do.

Graphing Linear Equations y is called the dependent variable because the value of y depends on x x is called the independent variable xy(x, y)

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

More Practice Ex3) The equation 10x + 5y = 40 models how you can give $0.40 change if you have only dimes and nickels. The variable x is the number of dimes, and y is the number of nickels. Graph the equation. Describe the domain and the range. Explain what the x- and y-intercepts represent.

Slope

Slope (cont.) What does it mean if the slope is zero? What does it mean if the slope is Undefined?

Point-Slope Form The line through the point (x 1, y 1 ) with slope m has the equation y – y 1 = m(x – x 1 )

Point-Slope Form The line through the point (x 1, y 1 ) with slope m has the equation y – y 1 = m(x – x 1 ) Ex7) Find the equation of a line through the points (-2, 3) and (1, 6). Then write it in standard form.

Slope-Intercept Form y = mx + b Ex8) 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?

Perpendicular Lines Ex9) Write an equation of the line through (5, –3) and perpendicular to y = 4x + 1. Graph both lines.

2.2: Linear Equations Our greatest glory is not in never falling, but in getting up every time we do. HW: # 1-15 odd, 20 – 36 even, 38-41