Answer:
The slope of the line is given, but we need to find the y-intercept to determine if the slope-intercept equation of this line would form a direct variation.
We can use the point-slope form of the equation of a line to find the y-intercept. The point-slope form is given by:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Substituting the given values, we have:
y - 2 = (1/3)(x - (-6))
y - 2 = (1/3)(x + 6)
y - 2 = (1/3)x + 2
y = (1/3)x + 4
Comparing this equation with the standard form of a direct variation y = kx, we can see that the equation does not have the same form. Therefore, the slope-intercept equation of this line would not form a direct variation.
Note that a direct variation has the form y = kx, where k is a constant of variation that remains the same for all values of x and y on the line. In other words, the ratio of y to x is constant for all points on the line.