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Determine la ecuacion de la recta que representa la siguiente grafica

To determine the equation of the line represented in the graph, we can use the general linear equation formula:

\[
y = mx + b
\]

where \(m\) is the slope of the line and \(b\) is the y-intercept.

### Step 1: Determine the Slope (\(m\))
The slope \(m\) is calculated by the change in \(y\) (rise) divided by the change in \(x\) (run) between two points on the line. The graph shows two clear points:
- Point 1: \((0, 5)\)
- Point 2: \((2, 3)\)

The slope \(m\) can be calculated as follows:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 5}{2 - 0} = \frac{-2}{2} = -1
\]

### Step 2: Determine the Y-Intercept (\(b\))
The y-intercept is where the line crosses the y-axis. From the graph, the line crosses the y-axis at \((0, 5)\), so the y-intercept \(b\) is 5.

### Step 3: Write the Equation of the Line
With \(m = -1\) and \(b = 5\), the equation of the line is:
\[
y = -x + 5
\]

This is the equation that represents the line in the graph.

Would you like any further details or explanations?

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Here are some related questions to explore:
1. How do you find the slope if the points are not as clear?
2. Can you determine the equation if only given the slope and a single point?
3. How does the slope affect the steepness of a line?
4. What happens if the slope is positive instead of negative?
5. How can you determine the x-intercept from the equation?
6. How does changing the y-intercept affect the graph of the line?
7. What is the significance of parallel lines in terms of their slopes?
8. How would you write the equation if the line was vertical or horizontal?

**Tip:** Always double-check the points selected from the graph to ensure accuracy in calculations!

Learn how to determine the equation of a line from a graph with a step-by-step guide. This problem covers finding slope, y-intercept, and writing the equation of a line. Suitable for Grades 7-9.

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