RWM102: Algebra

First, we need to understand the coordinate plane, the space in which we produce graphs. In this section we will focus on finding and graphing points on the coordinate plane to become comfortable with it.

Now we are ready to begin using graphs to determine if a pair of numbers (an ordered pair) is a solution to an equation.

A common way equations can be written is: Ax + By = C, where A, B, and C are numbers.

One of the properties of linear graphs is that they have intercepts on the x- and y-axis. The intercept is the point at which the line crosses the axis.

Another important property of linear graphs is the slope of the graph. The slope tells us how steep the line is. When a linear equation is written in a specific form that we’ll discuss later, the slope helps us determine how to graph the line.

Here, we learn about how the slopes of parallel and perpendicular lines are related. Parallel lines have the same slope, while perpendicular lines have slopes that are reciprocals.

One of the most common types of graph is that of a line with the form y = mx + b. In this form, m is the slope of the line, and b is the y-intercept of the line. When an equation is in this form, it is easy to plot the linear graph, so it is important to be able to recognize when an equation is in this form.

In the last section we discussed the slope-intercept form of a linear equation. We can also write linear equations in a form known as the point-slope form. This form works for when you want to make a line between two known points.

This form is: y − y₁ = m(x − x₁).

The last type of linear graphing we need to study is the graph of an inequality rather than an equation. When we graph inequalities, we must pay attention not only to the numbers and variables but also the inequality itself. That is, are we graphing a less-than, or greater-than inequality?