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We are able to find an equation of a line knowing its gradient and a point it passes through.


Let's say we want to find an equation of a line with a gradient 2, passing through the point (4, 5).


Start with a general equation of a straight line y = mx + c.

m represents the gradient, c represents the y-intercept.

We know the gradient, so we can replace m with 2.

This gives us y = 2x + c.


To work out the value of c, substitute the coordinates of the point given in the question.

The coordinates here are (4, 5), so x = 4 and y = 5.


5 = 2 × 4 + c

5 = 8 + c

5 - 8 = c

-3 = c


Now let's put everything together to get the equation y = 2x - 3.


It is also useful to know that parallel lines have the same gradient. You can use this property of straight lines when the question does not specifically tell you what the gradient is.

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