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2.4 Essential Questions

2.4 Essential Questions. What is the point-slope form? How do you write an equation if you are given a slope and y-intercept? How do you write an equation if you are given a point and a slope?

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2.4 Essential Questions

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  1. 2.4 Essential Questions • What is the point-slope form? • How do you write an equation if you are given a slope and y-intercept? • How do you write an equation if you are given a point and a slope? • How do you write an equation that is parallel or perpendicular to a given line if you are only given a point? • How do you write an equation if you are given two points?

  2. 2.4 Write Equations of Lines Point-slope form Slope – intercept form y =mx +b y –y1=m(x –x1)

  3. 3 4 3 4 From the graph, you can see that the slope is m = and the y-intercept is b = – 2. 3 y =x +(– 2) Substitute for mand –2 for b. 4 3 4 Writing an equation given the slope and y-intercept Write an equation of the line shown. Use slope-intercept form. y =mx +b y =x –2 Simplify.

  4. y =x +1 y =x + 1 3 3 Writing an equation given the slope and y-intercept m = 3, b = 1 Use slope – intercept form y =mx +b

  5. Writing an equation given the slope and y-intercept GUIDED PRACTICE m = – 2 , b = – 4 y =mx +b y =– 2x + (– 4 ) y = – 2x – 4

  6. 7 3 7 m = – b= 2 4 2 3 y = – x + 4 Writing an equation given the slope and y-intercept GUIDED PRACTICE y =mx +b

  7. Writing an equation given the slope and a point EXAMPLE 2 Write an equation of the line that passes through (5, 4)and has a slope of – 3. Because you know the slope and a point on the line, use point-slope form to write an equation of the line. y –y1=m(x –x1) point-slope form. Let (x1, y1) = (5, 4)and m = – 3. y –4=–3(x –5) y – 4 = – 3x + 15 y = – 3x + 19

  8. Writing an equation given the slope and a point GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through (– 1, 6)and has a slope of 4. y –y1 = m(x –x1) y –6 =4(x – ( – 1)) y – 6 = 4x + 4 y = 4x + 10

  9. How to write equations of parallel or perpendicular lines EXAMPLE 3 (use the point-slope form) Write an equation of the line that passes through (–2,3) and is parallel to the line y= –4x + 1. The given line has a slope of m= –4. So, a line parallel to it has the same slope of–4. Now you know the slope and a point on the line, so use the point-slope form with (x1,y1) = (– 2, 3) to write an equation of the line. y –y1=m2(x –x1) y –3=–4(x –(– 2)) y – 3 =– 4(x + 2) y – 3 =– 4x – 8 y =– 4x – 5

  10. 1 4 1 1 1 1 2 4 2 4 y –3= (x – (–2)) 1 y – 3 = (x +2) 4 1 4 y – 3 = x + y = x + How to write equations of parallel or perpendicular lines EXAMPLE 3 Write an equation of the line that passes through (–2,3) and is perpendicular to the line y= –4x + 1. A line perpendicular to a line with slope m= – 4 has a slope of y –y1=m2(x –x1)

  11. How to write equations of parallel or perpendicular lines GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1. A parallel slope would be3. y –y1 = m2(x –x1) y – (– 2) = 3(x – 4) y + 2 =3(x – 4) y + 2 = 3x – 12 y = 3x – 14

  12. 1 3 2 1 1 1 4 1 3 3 3 3 3 3 y – (– 2) =– (x – 4) y + 2 =– (x – 4) y + 2 =–x+ y = – x – How to write equations of parallel or perpendicular lines GUIDED PRACTICE A perpendicular slope is – Write an equation of the line that passes through (4, –2) and is perpendicular to the line y = 3x – 1. y –y1 = m2(x –x1)

  13. 12 – 3 10 – (– 2) y2 – y1 = m= x2 –x1 2 –5 How to write an equation given two points Write an equation of the line that passes through (5, –2) and (2, 10). First, find the slope = = – 4 Now you know the slope and two points on the line, so use point-slope form with either given point to write an equation of the line. y2– y1=m(x –x1) y–10=–4(x –2) y –10 = – 4x + 8 y = – 4x + 18

  14. – 7 – 5 = – 2 m = 4 –(– 2) How to write an equation given two points GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through the given points. (– 2, 5), (4, – 7) Find the slope Use that slope and one of the two points to find the equation of the line. y– y1=m(x –x1) y–7 =–2(x –4) y – 7 = – 2 (x – 4) y + 7 = – 2x + 8 y = – 2x + 1

  15. – 8 – 1 – 9 = = 1 m = – 9 – 3 –6 How to write an equation given two points GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through (6, 1), (–3, –8) y – y1=m(x – x1) y – (– 8))=1(x – (– 3)) y +8 = 1 (x + 3) y +8 = x + 3 y = x – 5

  16. 2 – y – 0=(x – 10) 11 0 – 2 2 2 – = m= – y = (x – 10) 11 11 10– (–1) 20 2 – y = x + 11 11 How to write an equation given two points GUIDED PRACTICE Write an equation of the line that passes through (–1, 2), (10, 0) y – y1=m(x – x1)

  17. HOMEWORK 2.4 p. 101 #3-16(EOP); 17, 20-25, 30-38, 40-45

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