point – slope & slope – intercept forms point – slope - uses a slope ( m ) and a point ( a, b...

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Point – Slope & Slope – Intercept Forms Point – Slope - uses a slope ( m ) and a point ( a , b ) to define a line y = m ( x – a ) + b Slope – Intercept – uses a slope ( m ) and a y – intercept ( b ) to define a line y = m x + b

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  • Slide 1
  • Point Slope & Slope Intercept Forms Point Slope - uses a slope ( m ) and a point ( a, b ) to define a line y = m ( x a ) + b Slope Intercept uses a slope ( m ) and a y intercept ( b ) to define a line y = m x + b
  • Slide 2
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 1, 6 ) with a slope ( m ) of
  • Slide 3
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 1, 6 ) with a slope ( m ) of - just replace ( m ) and ( a, b ) y = m ( x a ) + b y = ( x 1 ) + 6 a b
  • Slide 4
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( -5, 1 ) with m = y = m ( x a ) + b
  • Slide 5
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( -5, 1 ) with m = - replace ( m ) and ( a, b ) y = m ( x a ) + b y = ( x ( -5 )) + 1 y = ( x + 5 ) + 1
  • Slide 6
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line where m = - 3 and b = 2
  • Slide 7
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line where m = - 3 and b = 2 - substitute for m and b y = m x + b
  • Slide 8
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line where m = - 3 and b = 2 - substitute for m and b y = m x + b y = - 3x + 2
  • Slide 9
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line where m = and b =
  • Slide 10
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line where m = and b = - substitute for m and b y = m x + b y = x
  • Slide 11
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( - 3, 5 ) and ( 2, -2 )
  • Slide 12
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( - 3, 5 ) and ( 2, -2 ) Steps 1. Find the slope
  • Slide 13
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( - 3, 5 ) and ( 2, -2 ) Steps 1. Find the slope 2. Pick one of the points ( -3, 5 ) as ( a, b ) and use the slope you found in step one and substitute into y = m ( x a ) + b
  • Slide 14
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( - 3, 5 ) and ( 2, -2 ) Steps 1. Find the slope 2. Pick one of the points ( -3, 5 ) as ( a, b ) and use the slope you found in step one and substitute into y = m ( x a ) + b y = ( x ( - 3 )) + 5 y = ( x + 3 ) + 5
  • Slide 15
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( - 3, 5 ) and ( 2, -2 ) Steps 1. Find the slope 2. Pick one of the points ( -3, 5 ) as ( a, b ) and use the slope you found in step one and substitute into y = m ( x a ) + b y = ( x ( - 3 )) + 5 y = ( x + 3 ) + 5 NOTE : I like to use the point slope form for these problems. You can use slope intercept if you choose.
  • Slide 16
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 )
  • Slide 17
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 ) - Ill use slope intercept on this one Steps :1. Find the slope
  • Slide 18
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 ) - Ill use slope intercept on this one Steps :1. Find the slope We have part of our answer y = m x + b 2. Substitute m into eq. y = x + b
  • Slide 19
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 ) - Ill use slope intercept on this one Steps :1. Find the slope y = m x + b y = x + b 3. Using one of our points as ( x, y ) and substituting into our equation, we can find b 2. Substitute m into eq.
  • Slide 20
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 ) - Ill use slope intercept on this one Steps :1. Find the slope y = m x + b y = x + b 3. Using one of our points as ( x, y ) and substituting into our equation, we can find b
  • Slide 21
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 ) - Ill use slope intercept on this one Steps :1. Find the slope y = m x + b y = x + b 3.Using one of our points as ( x, y ) and substituting into our equation, we can find b 4.Substitute b
  • Slide 22
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 ) - Ill use slope intercept on this one Steps :1. Find the slope y = m x + b y = x + 7 3.Using one of our points as ( x, y ) and substituting into our equation, we can find b 4.Substitute b
  • Slide 23
  • Point Slope & Slope Intercept Forms Point Slope y = m ( x a ) + b Slope Intercept y = m x + b EXAMPLE : Find the equation of the line thru ( 6, - 2 ) and ( 4, 1 ) - Ill use slope intercept on this one Steps :1. Find the slope y = m x + b y = x + 7 Final Answer :
  • Slide 24
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form.
  • Slide 25
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for y = - 4x + 7
  • Slide 26
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for y = - 4x + 7 Since our equation is already in y = mx + b form, we just look for the m and b in their proper position.
  • Slide 27
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for y = - 4x + 7 Since our equation is already in y = mx + b form, we just look for the m and b in their proper position. mb
  • Slide 28
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for y = - 4x + 7 Since our equation is already in y = mx + b form, we just look for the m and b in their proper position. mb m = - 4 b = + 7
  • Slide 29
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for 2x + 3y = 10
  • Slide 30
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for 2x + 3y = 10 Our equation IS NOT in y = mx + b form, so we need to solve for y
  • Slide 31
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for 2x + 3y = 10 Our equation IS NOT in y = mx + b form, so we need to solve for y - subtracted 2x from both sides
  • Slide 32
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for 2x + 3y = 10 Our equation IS NOT in y = mx + b form, so we need to solve for y Divided by 3
  • Slide 33
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for 2x + 3y = 10 Our equation IS NOT in y = mx + b form, so we need to solve for y
  • Slide 34
  • Finding the slope ( m ) and y intercept ( b ) from a given equation. You must solve for y if the equation is not already in y = mx + b form. EXAMPLE : Find the slope and y intercept for 2x + 3y = 10 Our equation IS NOT in y = mx + b form, so we need to solve for y m b