GeoGebra Classroom

# Two Points to Linear Equations

Two points define a line and a line can be represented as a linear equation in several forms.
• The Point-Slope form
• The Slope-Intercept form
• The General Form
These equations are all linear equations, just different forms of the same equation. Stepping through the play button. 1. Two points define a line. Both points can be moved to make a new line 2. The slope of a line is the rise over the run. Here the slope is indicated by a triangle with a run of 1 3. The definition of slope can be used with the two points to solve for the slope 4. Another important point is where the line intercepts the y axis or the y-Intercept 5. The Slope-Intercept form uses the slope and y-intercept to make the linear equation. The y-intercept (b) can be solved from the slope and any point on the line. 6. The Point-Slope form can be solved from the definition of slope where (x,y) is any point on the line. 7. The General or Standard form puts both x and y on the same side of the equation. An expression is shown that gives a solution of the linear equation in standard form. This is a little tricky to derive. This form has a major advantage over the other two forms.

## Activities

After stepping through the steps. Move the points to the following values and note the line and the equations: ﻿ A = (0,0), B = (4,2) A = (0,0), B = (4,-2) A = (0,0), B = (2,2) A = (-2,-2), B = (4,4) A = (-2,2), B = (2,2) A = ( 2,-2), B = (2,2) What is the advantage of the general form? Is the specific equation for the general form unique? Can you multiply and equation by a number and still have an equivalent linear equation? Given the slope and intercept could you draw the line representing the linear equation?