Forms and Formulas for Lines

Let's talk about lines. In this post, I will talk about the various forms and formulas of lines. We will start with the slope formula.

We know with a line that a slope is constant. Its steepness is always the same.

This is the point-slope form. What if I take point-slope form, and plug in (0,b) , y-intercept, as the point.

Look, I got slope-intercept form.

Now, let's look at standard form:

Let's find the following
a. x-intercept (#,0)
b. y-intercept (0,#)
c. slope

a. x-intercept

For parts a and b, I can find the slope and y-intercept by solving for y, simplifying, and then comparing it to slope-intercept form.

Note on Forms and Formulas

The main difference between the two is a form describes all the points on the line. It describes the set of all points falling on the line. Whereas a formula results in a specified value given other values.

The slope formula is used to find the slope given two points. On the other hand, whether it is point-slope form, slope-intercept form, or standard form, it describes every point on the line. This is why the variables x and y are used. The form is true for every point (x,y) that satisfies the equation. (x,y) is varying on the line as the slope and a point are staying constant.

Review

For more on lines, check out my YouTube Videos.