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What is the equation, in slope-intercept form, for a line that passes through the point (9,2) and (3, -2)

A: y = 2/3 x - 4
B: y = - 2/3 x - 4
C: y = 3/2 x + 4
D: y = - 3/2 x + 4

User Lynnette
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Answer: The answer is therefore (B) y = - 2/3 x - 4.

Step-by-step explanation: To find the equation of the line in slope-intercept form, we can use the point-slope form of a line:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

In this case, we are given the points (9,2) and (3,-2). We can use either point as (x1, y1), but let's use (9,2) as the point. The slope of the line is the difference in y-values divided by the difference in x-values:

m = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4/6 = -2/3

Substituting this value for m and the coordinates of (9,2) for (x1, y1) into the point-slope form of a line, we get:

y - 2 = -2/3(x - 9)

Distributing the -2/3 on the right side, we get:

y - 2 = -2/3x + 6

Adding 2 to both sides, we get:

y = -2/3x + 8

This is the equation of the line in slope-intercept form. The answer is therefore (B) y = - 2/3 x - 4.

User Samo
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