Maths - Straight Line Graphs

Coordinate formulae for two points

What is the formula for the midpoint between two points?

\[(\frac{x _ 1 + x _ 2}{2}, \frac{y _ 1 + y _ 2}{2})\]

What is the formula for the distance between two points?

\[\sqrt{(y _ 2 - y _ 1)^2 + (x _ 2 - x _ 1)^2}\]

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 equation of a straight line?

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 substitute $m = 4$ 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 $(3, 4)$?

\[y = 2x - 2\]