Find the equation of the straight line which passes through the point (0, 3) and is perpendicular to the straight line with equation y = 2x.

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We know that a straight line has a general formula: y = mx+c, where m is the gradient of the line and c is the y-intercept; so, we are looking to find m and c. 

The line passes through the point (0,3) so x=0 and y = 3; thus, we substitute

3 = m * 0 + c; 

c = 3;

so, y = mx+3;

If y = mx+3 and y = 2x are perpendicuar, we know that the gradients of the 2 lines are negative reciprocals to each other and we can write m as:

m = -1/2;

Hence, y = -1/2x+3

Flavian M. A Level Maths tutor, GCSE Maths tutor

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