Question

What is the gradient of the line below?

Answer 1

Answer: -2

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Step-by-step explanation

Gradient = slope

The points (0,5) and (1,3) are on the line.

To go from (0,5) to (1,3), we do two things in either order:

• Go down 2 units
• Go right 1 unit

This motion of "down 2, right 1" leads to the slope -2/1 = -2 which is the final answer.

Recall that slope = rise/run.

The slope is negative because we go downhill as we move to the right.

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Another approach would be to use the slope formula.

`(x_1,y_1) = (0,5) \text{ and } (x_2,y_2) = (1,3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (3 - 5)/(1 - 0)\\\\m = (-2)/(1)\\\\m = -2\\\\`

The gradient is -2