Presentation on theme: "CHAPTER V Writing Linear Equations"— Presentation transcript:
1CHAPTER V Writing Linear Equations By:Uri HongMichael Yanoska
2Table of Contents 5-1 Slope-Intercept Form 5-2 Point-Slope Form 5-3 Writing Linear Equations given 2 points5-4 Standard Form5-5 Modeling with Linear Equations5-6 Perpendicular lines
3IntroductionThis chapter is about writing linear equations in a variety of algebraic forms including: slope-intercept form, point-slope form, and standard form.In this chapter, you will also use a linear model to solve equations and you will learn to write an equation perpendicular to another line.
45-1 Slope-Intercept Form y=mx+b (slope intercept form)m= the slopeb=y-intercept
5Finding the Slope (m)When given a graph, find two points on the graph (x1,y1)(x2,y2).To find the slope (m):Rise/Run= (y2-y1)/(x2-x1)To Find b (y-intercept)Look at the graph, and see where the graph crosses the y-axis.
6Example (slope-intercept) (x1,y1)(x2,y2)(0 , 0)(3, 2 )(y2 -y1)/(x2 -x1)= mm=(2-0)/(3-0)m = 2/3Y-intercept at (0,0)Plug into y =mx+by=(2/3)x + 0
75-2 Point-Slope Form y-y1=m(x-x1) You can use point-slope form to find a linear equation in slope-intercept form using the slope m and coordinates that are on the line.
8ExampleWrite in slope-intercept form the equation of the line that passes through the point (-3,7) with slope -2y-y1=m(x-x1)2. y-7= -2[x-(-3)]3. y-7=2x-64. y = -2x+1
9Just a side note (:When given a question asking to find an equation parallel, it means that the 2 equations will have the same slopey= 2x+3 and y= 2x+9 are parallelWhen given a question asking to find an equation perpendicular, it means that the 2 equations will have slopes that are opposite reciprocals.y= -2x +3 and y= (-1/2)x=6 are perpendicular.
10Writing Linear Equations given 2 Points Write in slope-intercept form the equation of the line that passes through the points (3,-2) and (6,0)Find the slope. Use (x1,y1)=(3,-2)(x2,y2)=(6,0)m=(y2-y1)/(x2-x1)[0-(-2)]/(6-3) =m= 2/3
12Standard Form The standard form of an equation of a line is Ax+By=C A and B = coefficients ≠0
13Write y=(2/5)x-3 in standard form with integer coefficients. ExampleWrite y=(2/5)x-3 in standard form with integer coefficients.Ax+By=Cy=(2/5)x-3multiply each side by y=5[(2/5)x-3]Distribute y=2x-15Subtract 2 from each side -2x+5y=-15Rewrite with leading Coefficient positiveHence: 2x – 5y = 15
14Modeling with Linear Equations A linear model = simulate a real life situation.The rate of change =compares the two entities that are changing.The slope = rate of change
15m=500 (slope= rate of increase) From the number of McDonalds in the U.S. increase by about 500 per year. In 2000, there were about 20,000 McDonalds. Write a linear model expressing the number of McDonalds.Let t=0 represent 1990m=500 (slope= rate of increase)t=10 (the year 2000)Therefore, (t1,r1)= (10,20000)y-r1=m(t-t1)y-20000=500(t-10)y-20000=500t-5000y=500t+15000
16Perpendicular LinesTwo lines are perpendicular if the 2 lines intersect and form a 90° angle.When given a question asking to find an equation perpendicular, it means that the 2 equations will have slopes that are reciprocals.y=2x +3 and y=(-1/2)x+6are perpendicular.
17Find the slope: (y2-y1)/(x2-x1) Find the slope that is perpendicular to the equation that has the following points: (3,2)(6,4) .Find the slope: (y2-y1)/(x2-x1)(4-2)/(6-3)= 2/32. Point-slope form : y-y1=m(x-x1)y-2=(2/3)(x-3)y-2=2/3x-2y=2/3x3. Find the slope perpendicular:m=2/3reciprocal= 3/2take the opposite= -(3/2)slope of the line perpendicular = -(3/2)
18Summary 5-1 Slope-Intercept Form (y=mx+b) 5-2 Point-Slope Form (y-y1=m(x-x1))5-3 Writing Linear Equations given 2 points5-4 Standard Form (Ax+By=C)5-5 Modeling with Linear Equations (real-life models)5-6 Perpendicular lines (opposite-reciprocal slopes)