Intersections of Lines
Solving a System’s Equations
A. Eliminate the variable
Solve for the variable
Plug back in
(#,#)
B. Solve for variable
Substitute
Plug back in
Point Slope Formula
y-y1=m(x-x1)
Slope Intercept Formula
y=mx+b
Standard Formula
ax+by=c
m=-a/b
1) 2x+5y=10
3x+4y=12
3(2x+5y=10)
2(3x+4y=12)
6x+15y=30
- 6x+8y=24
7y=6
y=6/7
2x+5(6/7)=10
2x+(34/7)=10
2x=5 5/7
x=20/7
(20/7,6/7)
2) y=3x+4
m=3
m,,=3
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Law of Cosines (used when you can't use Law of Sines):
ReplyDelete(opposite leg)^2 = (adjacent leg)^2 + (other adjacent leg)^2 - 2(adjacent leg) (adjacent leg) cos (angle between)
Example: you have a triangle with the sides of 5, 6, and 7. find the angle between 5 and 6.
7^2=6^2+5^2-2(5)(6)
cos a7^2-6^2-5^2= 2(5)(6)
cos acos a= 7^2-6^2-5^2 / -2(6)(5)
a= cos-1 ((7^2-^6^2-5^2)/(-2(5)(6))
a= 78.463 degrees
Law of Sines(used to non-right triangles):
Sin A/a = Sin B/b= Sin C/c
Example: you have a triangle with the sides 4 and 5 & you also have an angle of 30 degrees.
A = 1/2 (4) (5) Sin 30 degrees
A = 10 Sin 30 degrees which is aproximately = 5