Final answer:
The equation of the line passing through the points (-4,6) and (-2,0) is y = 3x + 18.
Step-by-step explanation:
To find the equation of the line passing through the points (-4,6) and (-2,0), we need to find the slope of the line. The slope, denoted as m, can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the given points, we have m = (0 - 6) / (-2 - (-4)) = 6 / 2 = 3. So, the slope of the line is 3.
Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), with either of the given points as (x1, y1). Let's use (-4,6) as (x1, y1):
y - 6 = 3(x - (-4))
y - 6 = 3(x + 4)
y - 6 = 3x + 12
y = 3x + 12 + 6
y = 3x + 18
Therefore, the equation of the line passing through the points (-4,6) and (-2,0) is y = 3x + 18.