Gradient-Of-A-Line Wjec-Eduqas Foundation

Gradient of a line

What is the gradient of a line?

• The gradient is a measure of how steep a straight line is

• A gradient of 3 means:

  • For every 1 unit to the right, go up by 3

• A gradient of -4 means:

  • For every 1 unit to the right, go down by 4 

• A gradient of 3 is steeper than 2

  • A gradient of -5 is steeper than -4

• A positive gradient means the line goes upwards (uphill)

  • Bottom left to top right 

• A negative gradient means the line goes downwards (downhill)

• Top left to bottom right

How do I find the gradient of a line?

• Find two points on the line and draw a right-angled triangle

  • Then

  • Or, in short,  

    • The rise is the vertical length of the triangle

    • The run is the horizontal length of the triangle

  • Put the correct sign on your answer

    • Positive for uphill lines

    • Negative for downhill lines

  • You can also find gradient of a line between two points,  and  

    • Use the formula <img alt=”fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction” data-mathml='<math ><semantics><mfrac><mrow><msub><mi>y</mi><mn>2</mn></msub><mo>-</mo><msub><mi>y</mi><mn>1</mn></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub></mrow></mfrac><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”59″ 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%2259%22%20width%3D%2260%22%20wrs%3Abaseline%3D%2236%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1da40657c9fece7e48d30af42d3’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAcmhlYWQQC2qxAAACAAAAADZoaGVhCGsXSAAAAjgAAAAkaG10eE2rRkcAAAJcAAAACGxvY2EAHTwYAAACZAAAAAxtYXhwBT0FPgAAAnAAAAAgbmFtZaBxlY4AAAKQAAABn3Bvc3QB9wD6AAAEMAAAACBwcmVwa1uragAABFAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAIhL%2F%2FwAAIhL%2F%2F93vAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAABAIABVQLVAasAAwAwGAGwBBCxAAP2sAM8sQIH9b