Final answer:
The slope-intercept form of the line passing through the points (-2, 11) and (3,9) is y = (-2/5)x + 51/5, found by calculating the slope and then solving for the y-intercept using one of the points.
Step-by-step explanation:
The equation in slope-intercept form for the line passing through the points (-2, 11) and (3,9) can be found by first calculating the slope (m) of the line and then using one of the points to solve for the y-intercept (b). To find the slope, use the formula m = (y2 - y1) / (x2 - x1), which gives us m = (9 - 11) / (3 - (-2)) = -2 / 5. Next, we use the slope-intercept form of the equation of a straight line, y = mx + b, and substitute one of the points and the slope to find the y-intercept. We can use point (3, 9), so 9 = (-2/5)(3) + b, hence b = 9 + 6/5 = 51/5. Therefore, the slope-intercept form of the equation is y = (-2/5)x + 51/5.