There are only a couple more items to cover relating to lines, so the notes for today will not be too long. However, the material from Days 8 and 9 are absolutely essential, and will be showing up in (nearly) every future math class you take — this is a good opportunity to make sure you understand it thoroughly and get your questions answered.
Horizontal and vertical lines are particularly simple — so simple, in fact, that they can be a little confusing. This video does a good job of explaining the graphs and equations of horizontal and vertical lines.
We saw last time how to write an equation for a line if we know the slope m and the y-intercept b (using the slope-intercept form, y=mx+b). It is often the case that we do not know the y-intercept, but instead we know a different point on the line. In this case, there is a shortcut that we can use to find the equation of the line — the point-slope form of a line, which is y-y1=m(x-x1) (m still represents the slope, and (x1, y1) is simply any point on the line).
This video gives some examples of writing equations of lines in point-slope form, and also talks about the similarities and differences between point-slope form and slope-intercept form.