Lines & Equations of Lines

In this chapter we'll go over everything you'd ever want to know about lines. The three major forms: slope-intercept form, point-slope form, and standard form. Horizontal and vertical lines. Graphing lines of all stripes. Finding the equation of a line through two points. And at the end we get into a common type of SAT question: Find the equation of a line that is perpendicular to another line.

How To Graph Lines (a.k.a. Linear Functions)

In this video we introduce the main standard equations of lines, and talk about how to graph them. The main takeaway will be: when in doubt, either solve for the x- and y-intercepts, or plug in a few x's to find a few points on the line, then connect the dots.

How to Find the Slope of a Line

Calculating slope, graphing slope. This video also gets into the slope special cases a bit, such as the slopes of vertical, horizontal, and perpendicular lines.

Horizontal & Vertical Lines

This video gets into the nitty gritty of horizontal and vertical lines. Why is there only one letter in them? How do you find the equation of a vertical line through a point? Why is the slope of a horizontal line zero, while vertical is undefined?

Slope-Intercept Form of a Line: y=mx+b

This is the line equation that everyone learns first, and therefore it's the first one that all my tutoring students try to use whenever lines are involved. Though that choice is yours, I will advocate for point-slope in the next video, because it really is better.

Standard Form of a Line: Ax+By=C

Not sure what's so "standard" about it. It has almost no meaning, and there's no situation in which one of the other two forms wouldn't be better! Yet they make you learn it, perhaps as some sort of throw-back to algebra methodologies of days gone by.

Point-Slope Form:
y-y1=m(x-x1)

I saved this for last because I want it to leave a lasting impression. From here on out, no matter what direction your academic career takes, this is the form of a line that will serve you the best in calculus, econ, business, you name it. Slope-intercept, step aside.

Equations of Parallel & Perpendicular Lines (free)

The SAT, in particular, emphasizes being able to find the equation of a line perpendicular to another line. [hint: "negative reciprocal" is gonna help] Later math and science classes use this property too, so it's not a complete waste of time.

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