Geometry and Trigonometry

Analytic Geometry

How is the slope measure and y-intercept of a line determined?

On a graph, the slope is the line in a plane completely specified by a point and a number. Mathematicians know that when an equation is written as y = mx + b, they can determine the slope measure and y-intercept (or slope intercept) of the line. In this case, the m (or x coefficient) is called the slope measure and the y-intercept are the coordinates that solve the equation.

For example, for y = -2x + 4, the slope measure is -2 and y-intercept is the coordinates (0, 4). To test this result, replace the x with the first coordinate (0); -2 × 0 = 0; therefore, 4 is left, resulting in y (or the y-intercept) being 4.


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