The set of all of the xy pairs that satisfy this equation and if you were to graph Now why do we call it a linear equation? Well if you were to take
So, for example the equation y is equal to two x minus three, this is a linear equation. And just to start ourselves out, let's look at some examples
Introduce you to in this video is the idea of a Linear Equation. We conclude that the graph of any linear equation in x and/or y is always a straight line. The slope is the constant m, so the graph of y=mx+b is a straight line. The distinctness of x_1 and x_2 avoids division by 0 when we find the slope. For any two distinct points on the graph, the x-coordinates, say x_1 and x_2, are also distinct (since the same value of x would give the same value of y because y is given explicitly in terms of x). This is clearly a vertical line through (a, 0).įor the form y=mx+b, if we can show that the slope is constant, then the graph must be a straight line. (Yes, this already includes the form where y is a constant, because this would be the result of taking m to be 0 in the equation y=mx+b).įor the form x=a, the graph is the set of all points with constant x-coordinate a. In x and/or y, any linear equation is equivalent to one of two forms: x=a or y=mx+b where a, m, and b are constants.
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