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Mth141S14n - Sec 1.4 Equations of lines linear models...

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Sec. 1.4 – Equations of lines & linear models Slope-intercept equation of a line : y = mx + b or f(x) = mx + b Any equation in 1 x and/or 1 y is called a linear equation (its graph is a straight line). Ex. x + y = 10 y= -3x + 2 y = 3 x = -2 Some other equations of lines that may be helpful to know are : Point-Slope equation : 1 1 ( ) y y m x x - = - this is from 2 1 2 1 y y m x x - = - . Two point equation : 2 1 1 1 2 1 ( ) y y y y x x x x - - = - - which is the above equation, but replacing m with its definition. Standard Equation of a line : There is a certain form of a line that is said to be the “standard” form of the equation of a line. A linear equation written in the form Ax + By = C where A, B, and C are real numbers, is called the standard form of the equation of a line. Generally we like A, B, and C to be integers. For example 3x + 2y = 8. Although this equation looks “pretty”(no fractions, or decimals), it doesn’t give us much information about the line. It doesn’t tell us easily the slope or the y-intercept. The slope-intercept form gives us more information. We can , of course, with a little algebra, change the form of the equation : 3 2 8 x y + = 2 3 8 y x = - + (-3x on both sides) 3 4 2 y x = - + ( ÷ 2 on both sides) So we see that the line has a y-intercept of 4 and a slope of 3 2 - . Given a line in y = mx + b form, you can reverse the above steps to change its form to “standard” form.
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