Direct-Proportion Aqa Higher

Direct proportion

What is direct proportion?

• Proportion is a way of talking about how two variables are related to each other

• Direct proportion means that as one variable goes up the other goes up by the same factor

  • The ratio between the two amounts will always stay the same

• The symbol means “proportional to”

  • E.g. y is directly proportional to x, yx

• If x and y are directly proportional, then

  • x : y will always be the same

  • there will be some value, k, such that y = kx

  • the graph relating x and y is a linear graph, with gradient k

• k is called the constant of proportionality

How do I use direct proportion with powers and roots?

• Problems may involve a variable being directly proportional to a power or root of another variable

• For example

  • y is directly proportional to the square of x

    • 

    • means that

  • y is directly proportional to the square root of x

    • <img alt=”y proportional to square root of x” data-mathml=”<math ><semantics><mrow><mi>y</mi><mo>&#8733;</mo><msqrt><mi>x</mi></msqrt></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”26″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2226%22%20width%3D%2255%22%20wrs%3Abaseline%3D%2220%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%26%23x221D%3B%3C%2Fmo%3E%3Cmsqrt%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmsqrt%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1502cc2c94be1a7c4ca7ef25b8b’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAABDGhlYWQQC2qxAAACmAAAADZoaGVhCGsXSAAAAtAAAAAkaG10eE2rRkcAAAL0AAAACGxvY2EAHTwYAAAC%2FAAAAAxtYXhwBT0FPgAAAwgAAAAgbmFtZaBxlY4AAAMoAAABn3Bvc3QB9wD6AAAEyAAAACBwcmVwa1uragAABOgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAIh3%2F%2FwAAIh3%2F%2F93kAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAACAE0AKALTAigAHQApAFMYAbAqELAL1LALELAa1LAaELAh1LAaELAV1LAVELAAPLAVELAr1ACwKhCwGtSwGhCwFtSwFhCwFdSwGhCwANSwABCwAdSwGhCwITywIRCwC9QwMQE3JgcGByYnJgcGFwYXFjc2NxYXFjcnJicmJzY3NgUWHwEHBgcGJyY3NgLSATpCNhwrMYCAWwUGXICCLykgNjhCATwtEysuFCr%2ByzMgJyceLFlIXl5GAbJMASQwNEAcVVVPXFxOVlIhRTsuKgZLAi4SS0kTKQsWLzo5LRUhOmdjOAABAAAAAQAA1XjOQV8PPPUAAwQA%2F%2F%2F%2F%2F9Y6E3P%2F%2F%2F%2F%2F1joTcwAA%2FyAEgAOrAAAACgACAAEAAAAAAAEAAAPo%2F2oAABdwAAD%2FtgSAAAEAAAAAAAAAAAAAAAAAAAACA1IAVQMgAE0AAAAAAAAAKAAAAQwAAQAAAAIAXgAFAAAAAAACAIAEAAAAAAAEAADeAAAAAAAAABUBAgAAAAAAAAABABIAAAAAAAAAAAACAA4AEgAAAAAAAAADADAAIAAAAAAAAAAEABIAUAAAAAAAAAAFABYAYgAAAAAAAAAGAAkAeAAAAAAAAAAIABwAgQABAAAAAAABABIAAAABAAAAAAACAA4AEgABAAAAAAADADAAIAABAAAAAAAEABIAUAABAAAAAAAFABYAYgABAAAAAAAGAAkAeAABAAAAAAAIABwAgQADAAEECQABABIAAAADAAEECQACAA4AEgADAAEECQADADAAIAADAAEECQAEABIAUAADAAEECQAFABYAYgADAAEECQAGAAkAeAADAAEECQAIABwAgQBNAGEAdABoACAARgBvAG4AdABSAGUAZwB1AGwAYQByA