In this Section:
In this section, we learn how to algebraically manipulate a linear equation in two variables into different forms. We start by officially learning about slope-intercept form. This form of a line: y = mx + b, allows us to easily identify the slope as: ‘m’ and the y-intercept as: ‘(0,b)’. There are many different uses for this form of a line. As we have previously seen, it is much easier to graph a linear equation in this format. Next, we turn to point-slope form. This form of the line is used when we know one point and the slope, or two points on the line. Point-slope form: y - y1 = m(x - x1). We can plug in our known point and the slope and solve for y to place the equation in slope-intercept form. We conclude our lesson by learning about standard form. This form of the line carries different definitions, based on the text. In most high school courses, the form is given as: ax + by = c, where a, b, and c are integers, a ≥ 0, a and b are not both zero, and a, b, and c share no common factor other than 1. Most higher level math courses are less strict on this definition. We have the format of: ax + by = c, where a, b, and c are real numbers and a and b are not both zero.