1. Flashback!
13.6 & 13.7 (Part 1)
Graphing Equations of Lines & Writing Equations of Lines
Geometry Honors- Watanabe
Point-Slope, Slope Intercept & Standard Form

2. Where m is the slope and b is the intercept
What we know so far….
Slope Intercept Form
Where m is the slope and b is the intercept

3. Where two points are given as (x1,y1) and (x2,y2)
What we know so far….
Slope
Where two points are given as (x1,y1) and (x2,y2)

4. Recall… Write equations
Slope-intercept form is:
Where m is the slope and b is the y-intercept
Example: Find the equation of the line with slope -2 and y-intercept 8
y = -2x + 8
Easy if I know the y-intercept… but if I don’t?

5. Might be new to some… Point- Slope form is:
Where m is the slope and (x1,y1) is the given point that the line goes through

6. Where does this equation come from?
Point- Slope Form
Point- Slope form is:
Where does this equation come from?

7. Using Point-Slope Form to graph1 2 4 3 5 -1 -2 -3 -4 -5
Slope is
Point is (2,3)

8. Manipulate Point-Slope Form to Slope-Intercept form
Simplify

9. Using Point-Slope Form to graph1 2 4 3 5 -1 -2 -3 -4 -5
Slope is
Point is (4,-3)

10. Manipulate Point-Slope Form to Slope-Intercept form

11. Your turn

12. Forms of a linear equation (You need to know these!)
Slope-intercept Form y = mx + b
Standard Form Ax + By = C
Point-Slope Form y – y1 = m(x – x1)

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

14. If given the a point and the slope,
There are two methods that are both
effective.
The time required and the number
of steps for the two methods is
comparable.
Know how to do both, but typically
Either will work just fine.

15. If given the a point and the slope,
Step 1
Method 1
use slope-intercept form.
Substitute –2 for m, 5 for x &
–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

16. If given the a point and the slope,
Method 2
use point-slope form.
(My preferred method to start with)
Substitute –2 for m, 5 for x1, and
–8 for y1; then simplify and solve
the equation for y .
y – y1 = m(x – x1)
y – (– 8) = – 2(x – 5)
y + 8 = –2x + 10
Example
m = –2, contains (5, –8)
y = –2x + 2

17. If given two points, Then use the slope and EITHER point to work
like the previous example.
y – y1 = m(x – x1)
y – 7 = – 5(x – 2)
y – 7 = –5x + 10
m = –5,
contains (5, –8) and (2, 7)
y = –5x + 17