1. TANGENT LINE/ NORMAL LINE
Aimen Abbasi and Jael Navarro

2. Tangent Line
(x, y)

3. 5 steps 1. Plug in x to your original equation 2. Derive
3. Plug in x to your derived equation
4. Plug in to point intercept form
5. Chang it to y – intercept form

4. STEP 1 y = x^3 - 2x + 5 at x=2 y = (2)^3 - 2(2) + 5 y = 9
- You are given:
y = x^3 - 2x at x=2
- To find y, you need plug in x to your original equation
y = (2)^3 - 2(2) + 5
y = 9

5. STEP 2
- Derive
y = 3x^2 - 2

6. STEP 3
- Plug in your x to your derived equation
y = 3(2)^
= 10
SLOPE!

7. STEP 4 y –y1 = m(x + x1) y –9 = 10(x + 2)
- Plug it in to Point Intercept Form
y –y1 = m(x + x1)
y –9 = 10(x + 2)

8. STEP 5
Change it into y intercept form
y= 10x - 11

9. Lets try another
- You are given
X^2 + 2x – 3 at (1, 0 )

10. Next Step 2 is
- Differentiate
2X + 2
- Plug it in
2(1) + 2
= 4
SLOPE!

11. Point – Slope Form y – 0 = 4 (x - 1) y = 4 x - 4 - Plug it in
- Change to standard y = mx +b
y = 4 x - 4

12. Graph your line
y = 4 x - 4

13. Lets Practice !
- Find the tangent lines of the following