Final answer:
The equation of the line passing through the points (-4,8) and (-2,2) is y = -3x - 4. This was determined by calculating the slope between the two points and then using the point-slope formula to derive the line's equation.
Step-by-step explanation:
To find the equation of the line passing through the points (-4,8) and (-2,2), we'll first calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). For our points, this will be m = (2 - 8) / (-2 + 4) = -6/2 = -3.
Next, we'll use point-slope form to create the equation of the line: y - y1 = m(x - x1). We can use either one of the given points; using point (-4,8), the equation becomes: y - 8 = -3(x + 4). To simplify, distribute the slope on the right-hand side: y - 8 = -3x - 12. Finally, add 8 to both sides to get the equation in slope-intercept form: y = -3x - 4.