1. Forms of a linear equation
Slope-intercept Form y = mx + b
Standard Form Ax + By = C
Point-Slope Form y – y1 = m(x – x1)

2. If given the slope and y-intercept,
use slope-intercept form.
Example
m = 5, b = 7 5 7
y = ___ x + ___

3. Review of Slope-Intercept Form
(B8) Writing the Equation of a Line
Review of Slope-Intercept Form
The slope-intercept form of a linear equation is
y = mx + b.
m represents the slope
b represents the y-intercept

4. Review of Slope-Intercept Form
Name the slope and y-intercept of each equation:
m = -4, b =3
m = , b = 5
Rewrite as y = -8x , m = -8, b =
Rewrite as y = 2x - 5, m = 2, b = -5
Rewrite as y = x + 0, m = , b = 0
Rewrite as y = 0x + 5, m = 0, b = 5
y = -4x + 3
y = 5 – x
8x + y =
4x - 2y =10
y = x
y = 5

5. Write the equation of a line given...
1. Slope and y-intercept
2. Graph
3. x - and y-intercepts
4. Slope and Point
Two Points

6. Find the Equation of the Line Given the Slope and y-intercept
Substitute m and b into y = mx + b
m = -3, b = 1
m = -2, b = -4
m = 0, b = 10
m = 1, b = 0
m = 0, b = 0
y = -3x + 1
y = -2x - 4
y = 0x + 10, y = 10
y = 1x + 0, y = x
y = 0x + 0, y = 0

7. Find the Equation of a Line Given the Graph
Find the y-intercept from the graph.
Count the slope from the graph.
To write the equation of the line, substitute the slope and y-intercept in the slope-intercept form of the equation.

8. Example 1
b = -3
m =
y = x - 3 x y +2 +3

9. Example 2
b = 1
m =
y = x + 1 x y +1 -2

10. Example 3
b = 4
m = 0/1= 0
y = 0x + 4, y = 4 x y

11. 3. 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.

12. Example Write the equation of the line with x-intercept 3
and y-intercept 2.
x-intercept 3 = (3, 0); y-intercept 2 = (0, 2)
Slope:
y = mx + b

13. If given the a point and the slope,
4. Find the Equation of the Line Given the Slope and a Point
If given the a point and the slope,
Step 1
Use slope-intercept form.
Substitute –2 for m, 5 for x, and
–8 for y; then simplify to find
the value of b.
y = mx + b
–8 = –2(5) + b
–8 = –10 + b
2 = b
Example
m = –2, contains (5, –8)
Step 2
Substitute –2 for m, and 2 for b.
y = –2x + 2

14. If given two points, 5. Find the Equation of the Line Given Two Points
First, find the slope using the slope formula.
Example
contains (5, –8) and (2, 7)
m = 15 –3
m = –5
m = 7 – -8
2 – 5

15. If given two points, Then use the slope and EITHER point to work
like the previous example.
y = mx + b
7 = -5(2) + b
7 = b
b = 17
m = –5,
contains (5, –8) and (2, 7)
y = –5x + 17

16. Example
Write the equation of the line that goes through the points (3, 2) and (5, 4).