y = m x + b 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

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

y = ( x – 1 ) + 6 Point – Slope & Slope – Intercept Forms Point – Slope y = m ( x – a ) + b Slope – Intercept y = m x + b a 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

y = m ( x – a ) + b 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

y = m ( x – a ) + b y = ( x – ( -5 )) + 1 y = ( x + 5 ) + 1 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

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

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 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

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 =

y = x 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

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 )

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

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 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

y = ( x + 3 ) + 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 ( - 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.

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 )

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 ) - I’ll use slope – intercept on this one… Steps : 1. Find the slope

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 ) - I’ll 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

y = m x + b y = x + b 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 ) - I’ll use slope – intercept on this one… Steps : 1. Find the slope y = m x + b y = x + b 2. Substitute m into eq. 3. Using one of our points as ( x , y ) and substituting into our equation, we can find b

y = m x + b y = x + b 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 ) - I’ll 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

y = m x + b y = x + b 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 ) - I’ll use slope – intercept on this one… Steps : 1. Find the slope y = m x + b y = x + b Using one of our points as ( x , y ) and substituting into our equation, we can find b Substitute b

y = m x + b y = x + 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 thru ( 6 , - 2 ) and ( 4 , 1 ) - I’ll use slope – intercept on this one… Steps : 1. Find the slope y = m x + b y = x + 7 Using one of our points as ( x , y ) and substituting into our equation, we can find b Substitute b

y = m x + b y = x + 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 thru ( 6 , - 2 ) and ( 4 , 1 ) - I’ll use slope – intercept on this one… Steps : 1. Find the slope y = m x + b y = x + 7 Final Answer :

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.

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

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.

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 m b Since our equation is already in y = mx + b form, we just look for the m and b in their proper position.

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 m = - 4 b = + 7 m b Since our equation is already in y = mx + b form, we just look for the m and b in their proper position.

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

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…

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

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

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…

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