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Coordinate Geometry and Vectors

Quick questions on Gradient and equation of a line explained: N(A)-Level Mathematics Coordinate Geometry and Vectors

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are the gradient between two points?
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The gradient measures steepness: how much yy changes for each unit of xx. For two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
What is the equation of a straight line?
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Every non-vertical straight line has the form:
What is checking the equation?
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Substitute the other point (or the given point) back into your equation. If both sides match, the line really does pass through that point and the equation is correct. This single check catches most arithmetic and sign slips, so it is always worth the few seconds it takes.
What are sign slips with negative coordinates?
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2−(−1)2 - (-1) is 33, not 11. Subtracting a negative adds.

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