2.4 writing equations of lines

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2.4 writing equations of lines

  1. 1. 2.4 Writing Equations of LinesObjectives:● I will write linear equations given the slope (m) and the y-intercept (b).● I will write linear equations given the slope (m) and a point (x 1 , y 1 ).● I will write linear equations given two points (x 1 , y 1 ) and (x 2 , y 2 ).
  2. 2. Review of Slope-Intercept FormThe slope-intercept form of a linear equation is y = mx + b.m represents the slopeb represents the y-intercept
  3. 3. Review of Slope-Intercept FormName the slope and y-intercept of each equation : y = -4x + 3 m = -4, b =3 1 1 y=5– x m=- ,b=5 2 2 3 3 8x + y = − 3 Rewrite as y = -8x − , m = -8, b = − 4 4 4 4x - 2y =10 Rewrite as y = 2x - 5, m = 2, b = -5 1 1 1 y= x Rewrite as y = 3 x + 0, m = 3 ,b=0 3 y=5 Rewrite as y = 0x + 5, m = 0, b = 5
  4. 4. Write the equation of a line given...1. Slope and y-intercept2. Graph3. Slope and one point4. Two points5. x - and y-intercepts
  5. 5. 1. Find the Equation of the Line Given the Slope and y-intercept●Substitute m and b into y = mx + b m = -3, b = 1 y = -3x + 1 m = -2, b = -4 y = -2x - 4 m = 0, b = 10 y = 0x + 10, y = 10 m = 1, b = 0 y = 1x + 0, y = x m = 0, b = 0 y = 0x + 0, y = 0
  6. 6. 2. Find the Equation of a Line Given the Graph• Find the y-intercept from the graph.• Count the slope from the graph. vertical change rise change in y = = horizontal change run change in x• To write the equation of the line, substitute the slope and y-intercept in the slope-intercept form of the equation.
  7. 7. Example 1● b = -3 3● m= 2 +2 x 3● y= 2 x-3 +3 y
  8. 8. Example 2● b=1 1● m= − 2 -2 +1 x 1● y= − 2 x+1 y
  9. 9. Example 3● b=4● m = 0/1= 0 x● y = 0x + 4, y = 4 y
  10. 10. 3. Find the Equation of a Line Given the Point and the Slope● Use the Point-Slope Formula: ( y − y1 ) = m( x − x1 )● ( x1 , y1 ) is the given point● Substitute m and ( x1 , y1 ) into the formula
  11. 11. Example● Write the equation of the line with slope = -2 and passing through the point (3, -5).● Substitute m and ( x1 , y1 ) into the Point-Slope Formula. ( y − y1 ) = m( x − x1 ) ( y − −5) = −2( x − 3) y + 5 = −2 x + 6 y = −2 x + 1
  12. 12. 4. Find the Equation of the Line Given Two Points● Calculate the slope of the two points. y2 − y1 m= x2 − x1● Use one of the points and the slope to substitute into the Point-Slope formula. ( y − y1 ) = m( x − x1 )
  13. 13. Example● Write the equation of the line that goes through the points (3, 2) and (5, 4). y2 − y1 m= ( y − y1 ) = m( x − x1 ) x2 − x1 4− 2 ( y − 2) = 1( x − 3) m= 5−3 y−2= x−3 2 m = =1 y = x −1 2
  14. 14. 5. Find the Equation of the Line Given the x- and y - intercepts● Write the intercepts as ordered pairs. The x-intercept 4 is the ordered pair (4, 0). The y-intercept -2 is the ordered pair (0, -2).● Calculate the slope.● Substitute the slope and the y-intercept (b) into the slope-intercept formula.
  15. 15. ExampleWrite the equation of the line with x-intercept 3and y-intercept 2.x-intercept 3 = (3, 0); y-intercept 2 = (0, 2) y2 − y1Slope: m= x2 − x1 y = mx + b 2−0 2 m= y = − x+2 0−3 3 2 −2 m= = −3 3

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