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Slope of a Line
pages 353 - 357 of Understanding Maths Book 1
The slope of a line is a measure of how steep it is, or its gradient.
Slope = Gradient = change in vertical height / change in horizontal length
= rise/run (rise, rises to the top; run on your feet)
Eg. If you rise 10 metres while walking 100m horizontally you have a slope of 0.1,
and if you draw a triangle and ask Pythagoras, a walk of 100m and 50cm along that
slope. Positive slope goes up right , negative slope goes down right.
On a Cartesian plane (a graph) the slope between two points can be calculated
from their coordinates. The two points are P(x1, y1) and Q(x2, y2) and the slope m,
is m = (y2 – y1)/(x2 – x1)
The slope between (1, 2) and (4, 5) = m = (5 – 2 )/(4 – 1 ) = 3/3 = 1
Note a vertical line does not have a slope as we can’t divide by zero.
Exercise 18.5 on p.356
1a) -1, b) 3, c) 1, d) 2/3 = 0.667, e) -1, f) vertical, g) 0.6, h) 0.
2, 3 see attached sheet
4, 5, 8, 9 Two lines are parallel if their slopes are the same.
6 ,7 The opposite sides of a parallelogram are parallel, and hence have the same
slope.
11 to 21, Substitute the numbers in the coordinates (2, 1) into the equation in place
of x and y and then check it adds up to the number shown.
2 + 1 = 3.
22 to 31 This is a bit more awkward it means that if we have an equation of a line
and know one of the coordinates of a point on the line we can work out the other.
Remember the first position is the x coordinate and y is the second coordinate. So
we get 22. (2, t) on 3x – y = 2, therefore 3*2 – t = 2, hence 6 – t = 2 or 6 – 2 = t
and so t = 4.