# Maths - Straight Line Graphs

What is the formula for the midpoint between two points?

\[(\frac{(x_2 - x_1)}{2}, \frac{(y_2 - y_1)}{2})\]

What is the formula for the distance between two points?

\[\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\]

- Pythagoras

What is the formula for the gradient between two points?

\[\frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}}\]

What are the two main ways of expressing the quation of a straight line?

- $y = mx + c$
- $ax + by + c = 0$

When using the $ax+by+c=0$ form of a straight line equation, there is an expectation that…?

$a,b$ & $c$ are integers.

What does it mean if points are collinear?

That the points all lie on a straight line.

What is the “magic” formula for a straight line with unknowns?

\[y - y_1 = m(x - x_1)\]

What is the formula for a straight line starting $y - y _ 1$?

\[y - y_1 = m(x - x_1)\]

How would you subsitute $m = 4$ and $(-2, 1)$ into the magic straight line formula?

\[y - 1 = 4(x - (-2))\]

What is the formula for a line with gradient $2$ and passing through $(3, 4)$?

\[y = 2x - 2\]