All you need for SAT Math Here!

by 974 Sep 15 2018

Thanks for reading, this is a port of a study guide that I am using to study for the SAT. This should be done soon, but I don't have that much time.


Slope = Rate of Change

Slope = $~$\frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}=tan\theta$~$

$~$y=mx+b\rightarrow slope=m$~$

$~$ax+by=c\rightarrow slope=\frac{-a}{b}$~$

negative slope $~$\rightarrow$~$ decreasing
positive slope $~$\rightarrow$~$ increasing
zero slope $~$\rightarrow$~$ constant/horizontal
undefined slope $~$\rightarrow$~$ vertical

Two parallel lines have the same slope but different y intercepts, no solution]
$~$y=mx+{b_1}, y=mx+{b_2}, {b_1}\neq {b_2}$~$

Two perpendicular lines, the product of two slopes equal -1
$~$y=mx+{b_1}, y=\frac{-1}{m}x+{b_2}$~$

Relation between two lines:

Line 1: $~${a_1}x+{b_1}y={c_1}$~$
Line 2: $~${a_2}x+{b_2}y={c_2}$~$

One Solution
$~$\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$~$

No Solution
$~$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$~$

Infinite Number of Solutions
Same Line

Equation of the Circle:

Standard Form: $~$\big(x-h)^2+\big(y-k)^2=r^2$~$
Center: $~$\big(h,k)$~$
Radius: $~$r=\sqrt{r^2}$~$

General Form: $~${x^2}+{y^2}+{ax}+{by}+c=0$~$
Center: $~$\big(\frac{-a}{2},\frac{-b}{2})$~$
Radius: $~$\sqrt{\big(\frac{a}{2})^2+(\frac{b}{2})^2-c}$~$

In addition:
Any point: $~$\big({x_1},{y_1})$~$
Inside: $~$\big(x_1-h)^2+\big(y_1-k)^2 On the Circle: $~$\big(x_1-h)^2+\big(y_1-k)^2=r^2$~$
Outside: $~$\big(x_1-h)^2+\big(y_1-k)^2>r^2$~$