1. 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

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

3. 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

4. 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

5. 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

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

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

8. 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

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 =

10. 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

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 )

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 Find the slope

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 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

14. 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 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

15. 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 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.

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 )

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

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 )
- 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

19. 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

20. 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

21. 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

22. 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

23. 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 :

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.

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

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.

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

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
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.

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

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…

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

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

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…

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