OpenAlgebra.com: Free Algebra Study Guide & Video Tutorials: algebra 1

Graphing lines can be done in a number of ways. This section describes a method, plotting points, that always works and can be used for many other types of equations. Notice that in a linear equation with two variables, y = 3x - 2, the y-value depends on what the x-value is. Since x is independent here, choose any real number, say x = 4, and you can find the corresponding y-value by evaluating y = 3(4) – 2 = 12 – 2 = 10. Therefore, the ordered pair (4, 10) is a point on the graph of the equation.

[ Free Printable Graph Paper ]

Example: Graph y = −2x + 6 by plotting five points.

Step 1: Choose any five x-values.
Step 2: Evaluate to find the corresponding y-values.
Step 3: Plot the points and use a straight edge to draw a line through them.

When choosing x-values it is wise to pick some negative numbers as well as zero. Try to find the points where the line crosses the x and y axes. These special points are called the x- and y-intercepts.

Is the given point a solution?

Remember that we are less likely to make a mistake if we insert parentheses where we see a variable and then substitute in the appropriate values.

Find the corresponding value.

Graph by plotting points.

Example: Graph y = 2x − 4 by plotting five points.

Example: Graph y = −x − 2 by plotting five points.

Choosing a scale when creating a blank coordinate system will take some thought. Keep in mind that the scale on the x-axis need not be the same as the scale on the y-axis.

Example: Graph y = 1/2 x − 6 by plotting five points.

When the coefficient of x is a fraction, choose x-values to be multiples of the denominator so that you might avoid unnecessarily tedious calculations.

Example: Graph y = −3/2 x + 6 by plotting five points.

Example: Graph 2x − 3y = 6 by plotting five points.

When dividing a binomial by a number you must divide both terms by that number. For example, treat the −3 as a common denominator as in the previous problem.

A common error is to just divide the 6 by −3.

Video Examples on YouTube:

Sometimes referred to as the rectangular coordinate system, the Cartesian coordinate system consists of two perpendicular real number lines intersecting at zero. Positions on this grid system are identified using ordered pairs, (x, y). The center of the system (0, 0) is called the origin. The x-coordinate indicates horizontal distance from the origin and the y-coordinate indicates vertical distance from the origin.

Instructional Video: Plotting Points on the Coordinate Plane

The horizontal number line, usually called the x-axis, is typically used for the independent variable. The vertical real number line, usually called the y-axis, is used for the dependent variable.

Ordered pairs with 0 as a coordinate do not lie in a quadrant; these points lie on an axis.

Example: Find the distance and midpoint between the two points: (3, 4) and (−1, 2).

Example: Find the distance and midpoint between the two points: (0, 0) and (−3, 4).

Example: Find the distance and midpoint between the two points: (−1,−1) and (1,1).

Example: Find the distance and midpoint between the two points: (−2,−5) and (−4,−3).

Circle Word Problem: If the diameter of a circle is defined by two points (−3, 4) and (7, 4), find the center and radius of the circle. (Hint: diameter = 2*radius)