Question

Find the equation of a line that passes through the point (-2,1) and has a gradient of -3.

Answer 1

A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.

We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is

y = mx + c...(1), where m is the gradient of the straight line and c is a constant.

Given that the gradient of the given straight line = m = -3.

Putting this value in (1), we get

y = -3x + c ...(2)

Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.

So, 1 = (-3)(-2) + c

i.e. 6 + c = 1

i.e. c = 1 - 6 = -5

(2) can be written as

y = -3x - 5

Therefore the equation of the given straight line is

y = -3x - 5

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