## 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* = -2*x* + 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.