# Linear Functions

Example 1: Graph the equation 2x + 5y = 10

Walpha Query: 2x+5y=10

Example 2: Find the equation of the line between (2,3) and (6,4).

Walpha Query: line through (2,3) and (6,4)

Example 3: Graph the line with a slope of -2 that passes through (3,1/2).

Walpha Query: line through (3,1/2) with slope -2

Example 4: Find the linear regression equation for the points (1,2.3), (2, 3.5), (3, 4.5), and (4,5.9).

Walpha Query: linear regression (1,2.3), (2, 3.5), (3,4.5), (4, 5.9)

## Result:

In each case Walpha graphs the linear function, gives the equation, gives properties of the line (slope and intercepts), and the distance between the points (where appropriate). For regression, you also receive a plot of the residuals.

## Implications:

The manipulation of equations (point-slope or slope-intercept form) is not required. As long as you know some basic characteristics of the line, Walpha will do the rest. Certainly, using Walpha to learn about the properties of linear functions would be helpful since both the graph, the equation, and the properties are shown (clearly connecting the concepts).