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Welcome to GCSE Edexcel Maths revision.

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Topic M 12: Coordinates and straight-line graphs.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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Coordinates open bracket x, y close bracket give horizontal position first, then vertical position.

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In quadrant I I, x is negative and y is positive; the origin is open bracket 0, 0 close bracket .

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The midpoint of open bracket x subscript open bracket 1 close bracket ,

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y subscript open bracket 1 close bracket close bracket and open bracket x subscript open bracket 2 close bracket ,

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y subscript open bracket 2 close bracket close bracket is open bracket the fraction with numerator open bracket x subscript open bracket 1 close bracket plus x subscript open bracket 2 close bracket close bracket and denominator open bracket 2 close bracket ,

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end fraction ,

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the fraction with numerator open bracket y subscript open bracket 1 close bracket plus y subscript open bracket 2 close bracket close bracket and denominator open bracket 2 close bracket ,

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end fraction close bracket .

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The midpoint of open bracket minus 2, 3 close bracket and open bracket 6, 7 close bracket is open bracket 2, 5 close bracket .

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A straight line has constant gradient m equals the fraction with numerator open bracket change in y close bracket and denominator open bracket change in x close bracket ,

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end fraction .

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Use two well-separated points on the line; a positive gradient rises to the right.

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Graph of y equals two x plus one

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Worked example: Through open bracket 1,

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3 close bracket and open bracket 4,

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9 close bracket ,

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m equals the fraction with numerator open bracket 9 minus 3 close bracket and denominator open bracket 4 minus 1 close bracket ,

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end fraction equals 2.

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Subtract the coordinates in the same order in numerator and denominator.

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In y equals mx plus c, m is the gradient and c is the y-intercept. y equals 2 x plus 1 passes through open bracket 0, 1 close bracket , and goes up 2 for every 1 across.

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To plot a line, calculate a table of values and draw a straight line through the points.

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Check the intercept and a third point to catch errors.

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A horizontal line is y equals k and has gradient 0.

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A vertical line is x equals k; its gradient is undefined because the horizontal change is zero.

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Worked example: A line with gradient 3 through open bracket 2, 5 close bracket has 5 equals 3 multiplied by 2 plus c, so c equals minus 1 and its equation is y equals 3 x minus 1.

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For a line through two points, find the gradient first, then substitute either point to find c.

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Through open bracket 1, 3 close bracket and open bracket 4, 9 close bracket , y equals 2 x plus 1.

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Parallel non-vertical lines have equal gradients. y equals 2 x plus 1 and y equals 2 x minus 5 are parallel; different intercepts make them distinct lines.

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Rearrange another line form to identify gradient: 2 y equals 6 x minus 4 becomes y equals 3 x minus 2, so the gradient is 3, not 6.

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For perpendicular non-horizontal, non-vertical lines, gradients satisfy m subscript open bracket 1 close bracket m subscript open bracket 2 close bracket equals minus 1.

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Take the negative reciprocal: the line perpendicular to gradient 2 has gradient minus 1 over 2 .

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Worked example: Perpendicular to y equals 2 x plus 1 through open bracket 4, 3 close bracket : y equals minus 1 over 2 x plus c.

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Substitution gives 3 equals minus 2 plus c, so y equals minus 1 over 2 x plus 5.

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A horizontal line is perpendicular to a vertical line.

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The negative-reciprocal rule should not be used by trying to divide by a zero gradient.

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That completes Coordinates and straight-line graphs.

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Revisit the notes and test yourself on the revision website.