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# Algebra I

Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
Community Questions
Graphing and analyzing linear functions
Use the power of algebra to understand and interpret points and lines (something we typically do in geometry). This will include slope and the equation of a line.
All content in “Graphing and analyzing linear functions”

### Coordinate plane

How can we communicate exactly where something is in two dimensions? Who was this Descartes character? In this tutorial, we cover the basics of the coordinate plane. We then delve into graphing points and determining whether a point is a solution of an equation. This will be a great tutorial experience if you are just starting to ramp up your understanding of graphing or need some fundamental review.

### Graphing solutions to equations

In this tutorial, we'll work through examples that show how a line can be viewed as all of coordinates whose x and y values satisfy a linear equation. Likewise, a linear equation can be viewed as describing a relationship between the x and y values on a line.

### x-intercepts and y-intercepts of linear functions

There are many ways to graph a line and this tutorial covers one of the simpler ones. Since you only need two points for a line, let's find what value an equation takes on when x = 0 (essentially the y-intercept) and what value it takes on when y = 0 (the x-intercept). Then we can graph the line by going through those two points.

### Proportional relationships

In this tutorial we'll think deeper about how one variable changes with respect to another. Pay attention because you'll find that these ideas will keep popping up in your life!

### Rates for proportional relationships

In proportional relationships, the ratio between one variable and the other is always constant. In the context of rate problems, this constant ratio can also be considered a rate of change. This tutorial allows you dig deeper into this idea.

### Slope

If you've ever struggled to tell someone just how steep something is, you'll find the answer here. In this tutorial, we cover the idea of the slope of a line. We also think about how slope relates to the equation of a line and how you can determine the slope or y-intercept given some clues. This tutorial is appropriate for someone who understands the basics of graphing equations and want to dig a bit deeper. After this tutorial, you will be prepared to start thinking deeper about the equation of a line.

### Graphing linear equations in slope-intercept form

Math is beautiful because there are so many way to appreciate the same relationship. In this tutorial, we'll use our knowledge of slope to actually graph lines that have been expressed in slope-intercept form.

### Constructing equations in slope-intercept form

You know a bit about slope and intercepts. Now we will develop that know-how even further to construct the equation of a line in slope-intercept form.

### Point-slope form and standard form

You know the slope of a line and you know that it contains a certain point. Well, in this tutorial, you'll see that you can quickly take this information (and that knowledge the definition of what slope is) to construct the equation of this line in point-slope form! You'll also manipulate between point-slope, slope-intercept and standard form.

### More analytic geometry

You're familiar with graphing lines, slope and y-intercepts. Now we are going to go further into analytic geometry by thinking about distances between points, midpoints, parallel lines and perpendicular ones. Enjoy!

### Graphing linear inequalities

In this tutorial we'll see how to graph linear inequalities on the coordinate plane. We'll also learn how to determine if a particular point is a solution of an inequality.

### Triangle similarity and constant slope

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. We'll connect this idea to the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b (cc.8.ee.6).

### Average rate of change

Even when a function is nonlinear, we can calculate the average rate of change over an interval (we'll need calculus to calculate the rate of change at a particular value of the independent variable). This tutorial will give you practice doing just that.

### Modeling with graphs

Much of the reason why math is interesting is that it can be used to model real-world phenomena. In this tutorial, we'll do just this with graphs.