# Maths - Straight Line Graphs

> Source: https://ollybritton.com/notes/a-level/maths/topics/straight-line-graphs/ · Updated: 2020-09-13 · Tags: maths, school, year-1

##### 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 $(3, 4)$??
$$
y = 2x - 2
$$

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