To find the correct slope-intercept form of the equation of the line given the points (8, 4) and (0, 2), we can follow these steps:
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Calculate the slope (m): The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] For points (8, 4) and (0, 2): \[ m = \frac{2 - 4}{0 - 8} = \frac{-2}{-8} = \frac{1}{4} \]
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Use point-slope form to write the equation: We can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] Using the point (8, 4): \[ y - 4 = \frac{1}{4}(x - 8) \]
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Convert to slope-intercept form (y = mx + b): Distributing on the right side: \[ y - 4 = \frac{1}{4}x - 2 \] Adding 4 to both sides: \[ y = \frac{1}{4}x - 2 + 4 \] \[ y = \frac{1}{4}x + 2 \]
Now, we can find the correct slope-intercept form from the options given:
- Correct answer: \[ y = \frac{1}{4}x + 2 \]
So, the slope-intercept form of the equation for this line is: \[ \boxed{y = \frac{1}{4}x + 2} \]