Final answer:
To find the slope-intercept form of the line passing through (2, -4) and (0, 4), we calculate the slope m as -4 and determine the y-intercept b as 4, resulting in the equation y = -4x + 4.
Step-by-step explanation:
The question involves finding the slope-intercept form of the equation of a line that passes through the points (2, -4) and (0, 4). The slope-intercept form of a linear equation is represented by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope m, we use the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (4 - (-4)) / (0 - 2) = 8 / (-2) = -4. With the slope found, we now know part of our equation is y = -4x + b.
Next, we need to find the y-intercept b. We plug in one of the points, let's use (0, 4), into our equation y = -4x + b. Thus, 4 = -4(0) + b leads to 4 = b. Now, we have our full equation: y = -4x + 4.