Questions: Find the equation of this line. Simplify your answer completely.

Find the equation of this line. Simplify your answer completely.
Transcript text: Find the equation of this line. Simplify your answer completely.
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Solution

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Solution Steps

Step 1: Identify the Slope

The slope (m) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

From the graph, the line passes through the points \((2, 4)\) and \((6, 0)\).

Step 2: Calculate the Slope

Substitute the coordinates of the points into the slope formula: \[ m = \frac{0 - 4}{6 - 2} = \frac{-4}{4} = -1 \]

Step 3: Identify the Y-Intercept

The y-intercept (b) is the value of y where the line crosses the y-axis. From the graph, the line crosses the y-axis at \(y = 6\).

Final Answer

The equation of the line in slope-intercept form \(y = mx + b\) is: \[ y = -1x + 6 \]

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