Questions: Consider the following function depicted in the following graph.

Consider the following function depicted in the following graph.
Transcript text: Consider the following function depicted in the following graph.
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Solution

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Solution Steps

Step 1: Identify the Slope

To find the slope of the line, we need to identify two points on the line. From the graph, we can see that the line passes through the points (0, 4) and (4, 0).

Step 2: Calculate the Slope

The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 4) and (4, 0): \[ m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1 \]

Step 3: Write the Equation of the Line

The equation of a line in slope-intercept form is: \[ y = mx + b \] We already have the slope \( m = -1 \) and the y-intercept \( b = 4 \) (since the line crosses the y-axis at (0, 4)).

Final Answer

The equation of the line is: \[ y = -x + 4 \]

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