$slope = m = \frac{y_1 - y_2}{x_1 - x_2} = \frac{y_2 - y_1}{x_2 - x_1}$
| Form Name | Equation |
|---|---|
| Slope Intercept | $y = mx + b$ |
| Point Slope | $y - y_1 = m(x - x_1)$ |
| Standard | $ax + by = c$ |
Positive slope is /
Negative slope is \
y = 0 is a horizontal line
x = 0 is a vertical line
$f(x - a)$ shifts the graph along the X-axis $a$ positions positive(to the right).
$f(x) + b$ shifts the graph along the Y-axis $b$ positions positive(upwards).
$f(ax)$ squeezes $f(x)$ by a factor of $a$
$f(\frac{x}{a})$ stretches $f(x)$ by a factor of $a$
$a x^2 + b x + c$
| Variable | Description |
|---|---|
| $a$ | $|a| > 1$ parabola narrower, $|a| < 1$ parabola wider, $a$ positive /\, and $a$ negative \/ |
| $b$ | $a$ positive and ($b$ positive left down or $b$ negative right down). $a$ negative and ($b$ positive right up or $b$ negative left up). |
| $c$ | $c$ positive shift upwards and $c$ negative shift down. |
$sin(x)$ starts at (0,0), peaks upwards($y = 1$) at $\frac{pi}{2}$, and is 0 at $pi$
$cos(x)$ starts at (0,1), peaks downwards($y = -1$) at $\frac{pi}{2}$, and is 0 at $pi$