How to solve linear equations in one variable from a graph.
This topic shows you how to solve algebra equations in one variable accurately by graphing. This method will often work even when you can't solve the equation using algebra.
An equation is a statement that two quantities are equivalent.
For example, this linear equation:
means that 5(x - 4) and 3x + 2 are exactly the same.
Only certain values of the variable 'x' will make the equation true. The process of finding out the variable value(s) that makes the equation true is called ‘solving’ the equation.
the left and right sides of the equation are graphed separately, the graphs will
intersect wherever the 'x' coordinate is a solution of the equation.
We will use the example described
in the ‘theory’ section above to demonstrate the steps for using Maths
Helper Plus to solve equations graphically.
Step 1 Start with an empty Maths Helper Plus document
If you have just launched the software then you already have an empty document, otherwise hold down ‘Ctrl’ while you briefly press the ‘N’ key.
Step 2 Split the equation into two halves
· If another symbol is used, replace with 'x'
· Split the equation into two halves at the equal sign. Write down two equations each starting with 'y =' followed by half of the original equation.
For example, taking our example equation:
From the left hand side, we have: y = 5(x - 4)
From the right hand side, we have: y = 3x + 2
Step 3 Enter the two equations
NOTE: You can type powers by using the '^' character. Type x2 as 'x^2', or x3 as 'x^3'.
· Type your first equation: y = 5(x - 4)
· Press the Enter key
· Type the second equation: y = 3x + 2
· Press the Enter key
For the example equations, the graph now looks like this:
Step 4 Adjust the graph scale
Depending on the equations you entered, important parts of the graphs may lie outside of the default graph scale. You can check on this with a simple zoom operation:
· Zoom out. Briefly press the F10 key one or more times until you are sure that all of the intersection points between the two graphs are visible.
· Zoom in. If you have zoomed out too far, hold down ‘Shift’ while you press F10 to zoom back in.
For the example graph, we must press F10 twice before the intersection point of the graphs is visible.
Step 5 Find the intersection points of the graph lines
· Select the intersection tool by clicking this button: on the 'math tools' toolbar.
The intersection tool dialog box will appear (see below) and the mouse cursor will have this shape: when the mouse is moved over the graph.
NOTE: If the intersection tool dialog box covers up part of your graph, you can move it. Point with the mouse to the title: 'Intersection Tool' at the top of the dialog box. Now click and drag to a new location.
· Move the cursor close to each point where the graph lines intersect. (See diagram) Click the left mouse button. If the intersection point was found, a black dot will appear on the graph, and the dialog box will display its coordinates.
· Write down the 'x' coordinate of the intersection point(s). These are the solutions of the equation.
· Cancel the intersection tool by clicking the 'Cancel' button on the intersection tool dialog box.