What is the gradient of the straight line passing through the points with coordinates (2, –3) and (–1, 6) ?
A. –1
B. – 9
C. – 3
D. -\frac{1}{9}
E. -\frac{1}{3}
In order to solve this, we will draw the straight line passing through those points:
To calculate the gradient we must divide the change in height by the change in horizontal distance
\text{Gradient} =\frac{\text{Change in Y}}{\text{Change in X}}
Therefore:
In our situation the Change in X is 3 and the Change in Y is -9.
[?] Why is the Change in Y negative? Since the line goes down as we move along (from left-to-right), the gradient is negative. Meaning UP is positive, and DOWN is negative.
\text{Gradient} =\frac{\text{Change in Y}}{\text{Change in X}} = \frac{-9}{3}= -3.
So the correct answer is (C)
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You can, by all means, not draw the graphic and just use the coordinates to calculate it.
In my opinion, it is better to draw, so you can see if it’s positive or negative with more ease.