Maths: Applications and Interpretation · Functions. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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The gradient of a line measures how steep it is: the change in y for each increase of 1 in x. A positive gradient goes up from left to right and a negative gradient goes down.
The same line can be written in three forms. y = mx + c shows the gradient m and the y-intercept c directly. The general form ax + by + d = 0 must be rearranged to read them. The point-gradient form is the quickest way to build an equation from a point and a gradient.
In a linear model the gradient is a rate of change (for example dollars per minute) and the intercept is the starting value when x = 0.
For a perpendicular line students only change the sign or only turn the fraction over. You must do both: perpendicular to gradient 3 is −1/3, not −3 and not 1/3.
Answer: y = −(1/2)x + 3
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