Slope - Algebra

Algebra

If y is a linear function of x, then the coefficient of x is the slope of the line created by plotting the function. Therefore, if the equation of the line is given in the form

then m is the slope. This form of a line's equation is called the slope-intercept form, because b can be interpreted as the y-intercept of the line, the y-coordinate where the line intersects the y-axis.

If the slope m of a line and a point (x₁,y₁) on the line are both known, then the equation of the line can be found using the point-slope formula:

For example, consider a line running through the points (2,8) and (3,20). This line has a slope, m, of

One can then write the line's equation, in point-slope form:

or:

The slope of the line defined by the linear equation

is: .