Final answer:
To write an equation in point-slope form, use the formula y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope. For the given points A(4, 2) and B(6, -3), the equation in point-slope form is y - 2 = -5(x - 4).
Step-by-step explanation:
To write an equation in point-slope form, we can use the formula: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope of the line.
Using the formula and the points A(4, 2) and B(6, -3), we can calculate the slope of the line:
m = (y2 - y1) / (x2 - x1)
m = (-3 - 2) / (6 - 4)
Once we have the slope, we can substitute the values of one of the points and the slope into the point-slope equation:
y - 2 = m(x - 4)
Therefore, the equation in point-slope form of the line that contains the given points A(4, 2) and B(6, -3) is: y - 2 = -5(x - 4).
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