📈 RAÍZ ó CERO de una FUNCIÓN LINEAL con FRACCIONES | Juliana la Profe

Summary

In this tutorial, viewers learn how to find the root (or zero) of a linear function by manipulating the equation and graphing it. The speaker demonstrates the process of setting y to zero, rearranging the equation, and solving for x, resulting in the root at 4.5. Additionally, the tutorial guides viewers through graphing the function, starting from the y-intercept and using the slope to identify another point. This visual representation highlights where the line intersects the x-axis, emphasizing the significance of the root. The video concludes by encouraging viewers to share and subscribe for more educational content.

Takeaways

• 😀 The video explains how to find the root (zero) of a linear function using a formula.
• 📈 Replacing 'y' with zero transforms the function into a linear equation.
• 🔍 The first step to isolate 'x' involves rearranging the equation by moving terms around.
• ➕ Adding 3 to both sides is necessary to eliminate the constant from one side of the equation.
• ✖️ Multiplying by 3 helps to clear the fraction and isolate 'x' effectively.
• 🔢 Dividing by 2 finalizes the calculation to find the root value of 'x', which is 4.5.
• 🗺️ The root can be visually represented on the Cartesian plane at the point where the line intersects the x-axis.
• 📊 To graph the function, start with the y-intercept and use the slope to find additional points.
• ✏️ The slope indicates how to move from the y-intercept to find another point on the line.
• 🎉 The video encourages viewers to share, subscribe, and look forward to more related content.

Q & A

What is the main topic of the video?

The video explains how to find the root or zero of a linear function using a formula and how to graph the function to visualize this zero on a Cartesian plane.

How do you find the root of the function?

To find the root, you replace y with zero in the equation, transforming it into a linear equation that can be solved for x.

What linear equation is used in the example?

The example uses the equation 0 = (2/3)x - 3.

What is the first step in solving the linear equation?

The first step is to isolate x by moving the constant term (-3) to the other side of the equation by adding 3.

What operation is applied to eliminate the division in the equation?

Multiplication is applied to eliminate the division; in this case, you multiply both sides by 3.

What value of x is found as the root of the equation?

The value found for x is 4.5, which is the root or zero of the linear function.

How is the root represented on the Cartesian plane?

The root is represented on the x-axis at the point (4.5, 0), where the line crosses the x-axis.

What point is used to start graphing the linear function?

The initial point used for graphing is the y-intercept, which in this case is -3, located on the y-axis.

How is the slope of the line determined from the equation?

The slope is determined from the coefficient of x, which is 2/3, indicating a rise of 2 units for every run of 3 units.

What is the significance of finding the root of a linear function?

Finding the root of a linear function is significant because it indicates the point where the function intersects the x-axis, representing the solution to the equation.