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0.2 Writing Linear Equation

0.2 Writing Linear Equation. Aug 24, 2012. Writing Equation of a line given. slope and y-intercept. plug in the number for the slope(m) and y –intercept (b) in the equation y = m x + b. Ex 1:. m=3 and y-intercept = 1. y = 3 x + 1. m=½ and y-intercept = -5. Ex 2:.

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0.2 Writing Linear Equation

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  1. 0.2Writing Linear Equation Aug 24, 2012

  2. Writing Equation of a line given slope and y-intercept plug in the number for the slope(m) and y –intercept (b) in the equation y = mx + b Ex 1: m=3 and y-intercept = 1 y = 3x + 1 m=½ and y-intercept = -5 Ex 2: y= ½x - 5

  3. Point Slope Form Equation of a line written in the form Where m is the slope and (x1, y1) is a point on the line Ex m= - 4 and (-2, 3) is a point on the line Ex m= 2/3and (4, -1) is a point on the line

  4. Standard Form Equation of a line written in the form Where A, B and C are whole number coefficients. Ex Standard to Slope Intercept Form

  5. Writing Equation of a line given slope and a point • Write the equation of the line in point slope form. • Simplify the right side. • Isolate y so that the equation becomes y= mx + b form.

  6. Write an equation of the line that passes through (4, 2) and has a slope of . 1 – 4 ( ) 4, 2 1 – Simplify the right side using distributive prop. – y 2 x 1 + = Use point-slope form with and m . 1 = = – 4 ( ) x1,y1 4 1 – y x 3 + = 4 ( ) Use point-slope form. – – y y1 m x x1 = 1 Substitute 2 for y1, 4 for x1and -¼ for m. ( ) – – – y 2 x 4 = 4 Example 2 +2 +2

  7. 1 ( ) 4, 2 – 4 Graphically Write an Equation Given Slope and a Point CHECK You can check the result by graphing the equation. Draw a line that passes through and has a slope of . Notice that the line has a y-intercept of 3, which agrees with the slope-intercept form found above.

  8. OR • Solve for b by substituting the x-coordinate of the point for x and y-coordinate for y and the slope for m in the equation y= mx + b • Now that you have b and m, write the equation of the line in y = mx + b slope and a point

  9. Write an equation of the line that passes through (4, 2) and has a slope of . 1 – 4 1 – y x 3 + = 4 Example 2 y = mx + b 2 = -¼ (4) + b 2 = -1 + b +1 +1 3 = b Substitute 2 for y, 4 for x and -¼ for m Simplify Solve for b

  10. ANSWER 1. ( ) 3 m 2 = , – – – – 3, 2, 1, 3 y 2x + 5 = ( ) 2 2 y 5x + 14 = m = 3 3 , 2. ( ) 4 m 5 = , 3. – y x 1 = More Examples: Write an equation of the line that passes through the given point and has the given slope. Write your equation in slope-intercept form.

  11. Writing Equation of a line given 2 points on the line • Find the slope between the 2 points using the slope formula • Pick one of the two points. Use that point for x and y in y = mx + b and the slope from step 1 to solve for b • Plug in the slope from step 1 and b from step 2 in y= mx + b.

  12. Write an equation of the line that passes through (2, 5) and (-2, 3). 1 y x 4 + = 2 Example 2 Solve for m using slope formula Pick a point to use for x and y. I picked this. y = mx + b 5 = ½ (2) + b 5 = 1+ b -1 -1 4 = b Substitute 5 for y, 2 for x and ½ for m Simplify Solve for b

  13. ANSWER y 3x + 2 = Another Example: Write an equation of the line in slope-intercept form that passes through the points (-2, -4) and (1, 5).

  14. Write an equation of the line that passes through and is parallel to the line . ( ) 4 – 1, The given line has a slope of 2. Any line parallel to this line will also have a slope of 2. – – y 2x + 5 = – Write Equations of Parallel Lines y = mx + b 4=-2(-1) + b 4 = 2+ b -2 -2 2 = b y = -2x + 2 Substitute 4 for y, -1 for x and -2 for m Simplify Solve for b

  15. Write an equation of the line that passes through and is perpendicular to the line . ( ) -1, 4 The given line has a slope of -2. The slope of any line perpendicular to this line will be the negative reciprocalof 2, which is ½ – y 2x + 5 = . 1 y x 4½ + = 2 Write Equations of Perpendicular Lines y = mx + b 4 = ½ (-1) + b 4 = -½+ b +½ +½ 4½ = b Substitute 4 for y, -1 for x and ½ for m Simplify Solve for b

  16. More Examples Checkpoint ANSWER – y x + 2 = – – – – 6, 5 6, 5 ( ( ) ) 2. passes through ; perpendicular to – y x + 2 = – – y x 11 = y x + 1 = Write an equation of the line described. 1. passes through ; parallel to

  17. Homework WS 0.2 Must be done on separate sheet of paper. Must be done in pencil. Must show work.

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