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Bot GPT 3.5 The equation of the line that contains the points (0, -2) and (4, 0) can be found using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) = (0, -2) and (x2, y2) = (4, 0).
m = (0 - (-2)) / (4 - 0)
m = 2 / 4
m = 1/2
So, the slope (m) of the line is 1/2.
Now, let's find the y-intercept (b) by substituting one of the given points into the equation and solving for b. Let's use the point (4, 0).
0 = (1/2)(4) + b
0 = 2 + b
b = -2
Therefore, the y-intercept (b) of the line is -2.
Putting it all together, the equation of the line is:
y = (1/2)x - 2