Gráfica de la función lineal | Ejemplo 1

How to Graph a Linear Function: y = 3x - 2

Introduction to Graphing Linear Functions

• The video introduces the concept of graphing linear functions, specifically focusing on the function y = 3x - 2.

• It emphasizes the importance of creating a Cartesian plane and using a table of values for plotting points.

Understanding Tables of Values

• A table of values is essential for graphing; it typically includes one column for x and another for y (or f(x)).

• While some educators prefer larger tables, starting with three values is sufficient to ensure accuracy in plotting.

Choosing Values for x

• Recommended simple values for x include 0, 1, and 2. Negative numbers can also be used if desired.

• It's advised to avoid large numbers as they may complicate the graphing process by placing points too high or low on the Cartesian plane.

Calculating y-values

• To find corresponding y-values, substitute chosen x-values into the equation. If not in standard form, it's suggested to rearrange the equation first.

• For example, substituting x = 0, we calculate:

• y = 3(0) - 2 = -2.

Plotting Points on the Graph

• Continuing with other values:

• For x = 1:

• Calculation yields y = 3(1) - 2 = 1.

• For x = 2:

• Calculation yields y = 3(2) - 2 = 4.

Ensuring Linearity in Graphing

• The importance of ensuring that plotted points are collinear is highlighted; three correctly calculated points should form a straight line.

• After plotting all three points (0,-2), (1,1), and (2,4), extend lines beyond these points to complete the linear representation.

Practice Exercise and Common Mistakes

• Viewers are encouraged to practice by graphing their own function based on provided coordinates.

• A common issue arises when locating points where one coordinate is zero; clarification is given on how to accurately place such points on axes.