How do I write

an equation of the line containing the given pair of points

How do I write

an equation of the line containing the given pair of points

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Since you are given 2 points of a line, the Point Slope form of a line can be used to solve the problem.

Y - Y_{1} = m (X - X_{1}) , m = the slope and (X_{1},Y_{1}) is one of the given points

Use the 2 points to find the slope

m = (change in Y) / (change in X) = (6-4)/(6-2) = 2/4 =1/2

Y - Y1 = m (X - X1)

Substitue the slope of 1/2 and the point at (6,6) gives

Y - 6 = 1/2 (X - 6)

Y - 5 = 1/2X - 3

Y = 1/2X + 2 This is the Y-intercept form of the line where 1/2 is the slope and intersects the y-axis at 2

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