Basic Formulas

Basic linear equation formula

Y M X C
Any Y value The Gradient The Corresponding X value The Y intercept

Gradient of a Line

Distance between two points

Midpoint

Non Linear Equations

Parabolas

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The basic equation for a parabola is
This creates the following parabola:
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Shifting a parabola vertically

To shift it vertically upwards by one, add one to the original equation to produce , to shift downwards, take one away.

Shifting a parabola horizontally

To shift a parabola horizontally, you use an equation like the following, which shifts it to the right by two: ; if you wanted to shift it to the left, use plus, not minus.

Circles

Basic formula:
radius is the length from the centre to any given point on the outline.

Calculating gradient

Basic formula:

Sketching

Linear

  1. Take as an example.
  2. Plot the point , 6 is our Y intercept.
  3. Convert the gradient to a fraction,
  4. Now plot a point that is 4 points up on the Y Axis, and 1 point over on the X axis.
  5. Repeat step four, but in reverse, 4 points down, one point to the right.
  6. Now draw a line between the points
    You should end up with an image like the below
    Pasted image 20240730204152.png

X and Y intercept method

let our formula be
to get our X intercept, let Y be 0, , now divide both sides by the multiplier on the X,
to get our Y intercept, let X be 0, , now divide both sides by the multiplier on the Y,
Our X intercept is (-2, 0) and our Y intercept is (0,1)
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If equation ends in = 0, it is a vertical line from top left > bottom right in the center.