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Chapter 5 Writing Linear Equations

By Anna Mullane
by

Anna Mullane

on 9 January 2013

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Transcript of Chapter 5 Writing Linear Equations

Writing Linear Equations Chapter 5 Slope-Intercept Form Point-Slope Form Fitting a Line to Data Equations of Parallel and Perpendicular Lines Predicting with Linear Models y=mx+b Writing an Equation of a Line Example: slope y-intercept Write an equation of the line whose slope is -1 and y-intercept is 3. Solution: 1) y=mx+b 2) y=-1x+3 Write slope-intercept form Substitute -1 for m and 3 for b Standard Form Summary of Equations THE END! Writing an Equation of a line Given its Slope and a Point Writing an Equation of a Line when Given Two Points y-y =m(x-x ) 1 1 slope given point (nonverticle line) Ax+By=C real numbers not both zero Slope-Intercept Form: Point-Slope Form: Verticle Line (undefined slope): Horizontal Line (zero slope): Standard Form: y=mx+b y-y =m(x-x 1 1 ) x=a (x coordinate) y=b (y coordinate) Ax+By=C (A, B, and C are real numbers and A and B are not both zero) Example: Write an equation of the line that passes through the point (3,4) and has a slope of 2. Solution: 1) y=mx+b Find the y-intercept 2) 4=(2)3+b 3) 4=6+b 4) -2=b Write an equation 1) y=mx+b 2) y=2x-2 Write slope-intercept form Substitute Solve Write slope-intercept form Substitute Simplify Example: Write an equation that passes through
the points (1,2) and (2,5). Find the slope Find the y-intercept Write an equation Solution: 1) m=y -y x -x 1 2 1 2 Write formula 2) m=5-2 2-1 Substitute Simplify 3) m=3 1 =3 Write slope-intercept form 1) y=mx+b Substitute Simplify Solve 2) 2=(3)1+b (choose either point) 3) 2=3+b 4) -1=b Write slope-intercept form Substitute 1) y=mx+b 2) y=3x-1 Using Point-Slope Form Example: Write an equation of the line that passes through the points (2,3) and (3,2). Solution: 1) m=2-3 Find the slope (choose either point) Write point-slope form Substitute Use distributive property Solve 3-2 = -1 1 = -1 2) y-y =m(x-x ) 1 1 3) y-3=-1(x-2) 4) y-3=-1x+2 5) y=-x+5 Writing an Equation in Standard Form Writing a Linear Equation Determining the Correlation of a Set of Data Positive Correlation Negative Correlation Relatively No Correlation Approximating a Best-Fitting Line To draw a best-fitting line, sketch the line that appears to best fit the points Best-Fitting Line: The line that best fits a set of data Two nonverticle lines are parallel only if they have the same slope. Two nonverticle lines are perpendicular only if their slopes are negative reciprocals of each other. Which Data Set Is More Linear? You can see that the data set on the right falls almost directly on a straight line, therefore it is more linear. Example: Write y=2x+3 in standard form with integer coefficients. Solution: Write original equation 1) y=2x+3 2) y-2x=3 Subtract 2x from each side Write in standard form 3) -2x+y=3 Example: Write the standard form of the line passing through (2,5) and has a slope of 3. Solution: 1) y-y =m(x-x ) 2) y-5=3(x-2) Write point-slope form Substitute Use distributive property 3) y-5=3x-(3)2 Simplify 4) y=3x-11 Write in standard form 5) -3x+y=-11 Linear Interpolation A method of estimating the coordinates of a point that lies between two given data points. Linear Extrapolation A method of estimating the coordinates of a point that lies to the right or left of all the given data points. Anna Mullane 1 1
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