Mathematics GCSE - Module 5

Always do X-axis first.

Line A - (5,6) (0,6) (-3, 6)  y=6

Line B - (1,1) (5,1) (-5,1)  y=1

Line C - (0,4) (0,2) (0,1)  X=0

Line D - (5,2) (5,1) (5,-3) X=5

For verticle or horizontal they will always be the form x=? or y=?

Always use pairs of coordinates.

Straight lines on a diagonal.

e.g Y=2x+1    (1,3) (2,5) (3,7)

so its 2 multiplied by X and adding one. For example 1x2=2+1= 3 and 2x2=4+1=5

Methods for drawing linear graphs

• 1) Pick 3 pairs of co-ordinates
• 2) Identify the gradient and intercept.
• 3) use the x=0 and y=0 method for graphs written in the form of 2x+3y

y=x — (1,1) (2,2) (3,3) (4,4)

y=x+2 — (1,3) (2,5) (3,7)

y= 3x+2 — (1,0) (2,3) (3,6)

y= -2 +2 — (1,0) (2,-2) (3,-4)

y=mx+c  c= y-intercept   m=steepness/gradient.

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m=3/5 so imagine that that line above is 3 squares high and 5 squares wide. The steepness equals 3 divided over 5 ( the fraction 3/5) and that would be your answer.

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m= 5/3 which =1 2/3 (it became a top-heavy fraction so I converted it to normal fraction with a whole number at the front).

You can have positive and negative gradients. A positive gradient(e.g 2) would slope up and a negative(e.g -1) would slope down.