Final answer:
The slope-intercept form for the line passing through the points (5, 4) and (6, -1) is y = -5x + 29, with a slope of -5 and a y-intercept of 29.
Step-by-step explanation:
To write an equation in slope-intercept form for the line that passes through the points (5, 4) and (6, -1), we first need to calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (-1 - 4) / (6 - 5) = -5. With our slope, we can then use the point-slope form, y - y1 = m(x - x1), to create an equation based on one of our points, let's choose (5, 4). This yields y - 4 = -5(x - 5). Expanding this, we get y - 4 = -5x + 25. Finally, adding 4 to both sides gives us the slope-intercept form: y = -5x + 29.