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.