Answer: -3.
Step-by-step explanation: To solve this problem, we need to find the value of w, which is the y-coordinate of the point (–4, w) on the line with a slope of 6. We can do this by using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line, x and y are the coordinates of a point on the line, and b is the y-intercept (the point where the line intersects the y-axis).
In this case, we are given that the slope of the line is 6 and that the line passes through the point (–4, w). We can use this information to write the equation for the line as: y = 6x + b
Substituting the coordinates of the point (–4, w) into the equation, we get: w = 6 * (-4) + b
Solving for b, we get: b = w - 24
Next, we are given that the line also passes through the point (–3, 9). Substituting the coordinates of this point into the equation for the line, we get: 9 = 6 * (-3) + b
Substituting the value of b that we found earlier, we get: 9 = 6 * (-3) + w - 24
Solving for w, we get: w = -3
Therefore, the value of w is -3.