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Bot GPT 3.5 To find the y-intercept of the line passing through the points (0, 4) and (4, 2), we first need to determine the equation of the line.
The slope of the line can be found using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) = (0, 4) and (x2, y2) = (4, 2).
slope = (2 - 4) / (4 - 0) = -2 / 4 = -1/2
Now we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the given points.
Using the point (0, 4), we get: y - 4 = (-1/2)(x - 0)
Simplifying the equation: y - 4 = -1/2x
To find the y-intercept (where x = 0), we plug in x = 0 into the equation:
y - 4 = -1/2(0)
y - 4 = 0
y = 4
Therefore, the y-intercept of the line passing through the points (0, 4) and (4, 2) is 4.