By J. Newbury PhD (auth.)
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The line cuts the y axis at the point A, that is, where y is 1, and having found this point we can use the gradient to find the co-ordinates of any other point. The gradient teHs us the change in y for an increase of 1 in x, so in our case since the gradient is 2 the y co-ordinates of points on the line increase at the rate of 2 for each increase of 1 in x (or change in y is twice the change in x). So if we start at A whose x co-ordinate is zero, moving to B means an increase of 1 in x; hence y increases by 2 so the y co-ordinate of B is 1 + 2 = 3.
Indicate the appropriate answer for each problem by evaluating each problem: -5 -6 = 11 (ü) -8 + 3 =-5 (ili) -7 - (+5) = 12 (i) (iv) -5 - (-8) (v) =3 (--6) x (-7) = 42 (iv) -(-8) x 5 = 40 (vii) -3 x (-4) = -12 (vili) 8 + -2 = -4 (ix) -9 + -3 = 3 (x) (--6)2 = 36 52 Basic Numeracy Skills 11 Basic Algebra 3. Formulae (i) If a train travels S metres in t seconds find the distance it travels in x minutes. (ii) If a m 2 of sheet metal has a mass of x kg what will be the mass of b m 2 ? ;(1). Find t when = 10.
The latter method is usually the one preferred since it will always yield an exact solution if a solution exists. This algebraic method outlined is not the only algebraic method available; there are others which vary slightly, but the basic idea is the same. RECIPROCALS ..!. x Exercise 135: Exercise 136: How could you show fairly easily that the graph y = I/x is not a straight line (that is, that the function is not linear? ) Sketch the graph using your results to Exercise 136. ) What happens when x = O?