Equations of Lines

In this lesson, we will look at the three different equations of a line. We will begin with slope-intercept form, which we can obtain by solving a linear equation in two variables for y. This gives us y = mx + b, where m is the slope and the y-intercept occurs at (0,b). In some cases, we will not be given enough information to immediately put a line in slope-intercept form. For these scenarios, we are often given a slope and a point on the line or two points on the line and no slope. When this occurs, we can use the point-slope form. This form y - y₁ = m(x - x₁) allows us to plug in the known point for (x₁,y₁) and our known slope m and obtain our slope-intercept form by solving for y. Lastly, we will run into standard form. With standard form, the definition varies from textbook to textbook. Essentially, we see standard form as: ax + by = c, where a, b, and c are integers and a is non-negative. Again this could be relaxed to say a, b, and c are just real numbers. When working with an equation in standard form, we can see that the slope occurs at: m = -a/b and our y-intercept occurs at: y-int: (0, c/b).