Final answer:
The equation in slope-intercept form for the line passing through (1, 6) and (4, -3) is y = -3x + 9.
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept. To find the equation in slope-intercept form for the line that passes through the points (1, 6) and (4, -3), we need to first find the slope using the formula m = (y2 - y1) / (x2 - x1). Substituting the values of the two points, we get: m = (-3 - 6) / (4 - 1) = -9 / 3 = -3. Then, we can use the point-slope form y - y1 = m(x - x1), substituting one of the points and the calculated slope. Taking (1, 6) as our point, the equation becomes: y - 6 = -3(x - 1). Simplifying, we get: y - 6 = -3x + 3. Finally, rearranging the equation to the slope-intercept form, we have: y = -3x + 9.