Sketch graphs

Straight line




You can also let y=0 and calculate x to draw the line.

The Circle




The Ellipse




The Parabola




The Hyperbola


Solve simultaneous equations graphically

Equations of straight lines

Two point form





One point and a gradient (Point slope form)





The distance between two points

,



The midpoint of a line segment

,

Different forms of the Straight line

The Gradient(Slope)-intercept form

$y=mx+c$

Where m = gradient = difference in y divided by the difference in x





The Intercept form





http://www.vitutor.com/geometry/line/intercept_form.html

The General form

$ax+bx+c=0$
$\mathrm{<br>}$ $$

Angle between points is given

If you are given an angle (Θ) and you must determine the gradient: The tangent of the angle is the gradient of the line: tanΘ = m


The equation is given

$y=mx+c$
m is the gradient.

Two points are given

$m=\frac{y_2-<!--\; -\; -->y_1}{x_2-<!--\; -\; -->x_1}$



Parallel lines
If two lines are parallel, their gradients are the same.




Perpendicular lines
If two lines are perpendicular, their gradients are opposite and inverse of one another.