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