Slope:

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
$\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$
Intersect

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

Infinite Number of Solutions
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
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: $\big(x_1-h)^2+\big(y_1-k)^2>r^2$