Final answer:
To find the value of w, we can use the slope-intercept form of a linear equation: y = mx + b. We need to find the y-intercept and solve for w by substituting the coordinates of the points on the line.
Step-by-step explanation:
To find the value of w, we can use the slope-intercept form of a linear equation: y = mx + b. In this equation, m represents the slope and b represents the y-intercept. We are given that the slope, m, is -(3/10). Moreover, we have two points on the line: (w, 3) and (-4, 6). Plugging in the coordinates of the second point into the equation, we can solve for b:
6 = -(3/10)(-4) + b
6 = 12/10 + b
6 = 6/5 + b
b = 24/5 - 6/5
b = 18/5
Now that we know the y-intercept, we can plug in the coordinates of the first point and solve for w:
3 = -(3/10)w + 18/5
3 - 18/5 = -(3/10)w
(15 - 18)/5 = -(3/10)w
-3/5 = -(3/10)w
w = (-3/5) / (-(3/10)) = 2