8th Grade Algebra: Help and Examples

Help with 8th Grade Algebra

Linear Equations

In 8th grade, you'll learn to graph linear equations, which are equations that can be represented by a straight line on the coordinate plane. Linear equations usually have two variables, x and y. Each pair of coordinate points (x, y) on the corresponding line can be substituted for those variables in the equation to make it true. For example, the line representing the equation y = 2x + 1 passes through the coordinate points (3, 7). When these values are plugged into the equation, they make it true.

x = 3; y = 7

y = 2x + 1

7 = 2(3) + 1

7 = 6 + 1

7 = 7

Graphing Equations

You can graph linear equations when they are in slope-intercept form, which looks like this: y = mx + b. Of course, in a 'real' equation, like y = 2x + 1, the 'm' and the 'b' will be replaced by numbers, which indicate the line's slope (m = 2) and y-intercept (b = 1). Together, these two bits of information can help you graph the line.

Y-intercept

The y-intercept (b) is the point where the line crosses the y-axis (the main vertical line on the graph). For the equation y = 2x + 1, the y-intercept is (0, 1). You can start at this point and then use the line's slope to graph it.

Slope

Slope (m) is equal to (change in y)/(change in x) for any two points on a line. It's often called 'rise over run.' Lines where the 'rise' (change in y) is larger than the 'run' (change in x) will be steeper. Alternatively, lines where the 'rise' is smaller than the 'run' will be closer to horizontal. In an equation like y = 2x + 1, where the slope is a whole number (two), you can assume that the change in x is equal to one because m = 2 and 2 = 2/1.

If the slope is 2/1, this means the next point on the line after the y-intercept (0, 1) is over one unit and up two units from that point, at (1, 3). From there, you can repeat this process to find the next point, (2, 5), and the one after that, (3, 7). A continuous straight line that passes through these four points is the graphical representation of the equation y = 2x + 1.

Plug-and-Chug

If an equation is not already in slope-intercept form, you can either transform it through manipulation, or you can use the 'plug-and-chug' technique to graph it. This simply means plugging in a randomly selected value for one variable and solving for the other variable. Each time you do this, you'll find another coordinate point that the line passes through. After you've identified and plotted several of these, you can draw a line through them to represent the equation.