Final answer:
To find the slope-intercept form from two given points, calculate the slope and then use one of the points to find the y-intercept. In this case, the slope is 1/2, and using the point (1, 3), the slope-intercept form is y = 0.5x + 2.5. However, the exact form does not match any provided options, indicating a potential error in the question or answer choices.
Step-by-step explanation:
The slope-intercept form of the equation of a straight line is typically written as y = mx + b, where m represents the slope and b represents the y-intercept. To find the slope (m), we can use the given points (-9, -2) and (1, 3). The slope is the change in y divided by the change in x, calculated as (3 - (-2))/(1 - (-9)), which simplifies to 5/10 or 1/2. With the slope known, we substitute a given point into the slope-intercept equation using the slope. We can use the point (1, 3) and the slope 1/2 to get: y - 3 = (1/2)(x - 1).
Once we distribute the slope on the right-hand side, we get y - 3 = (1/2)x - (1/2). To isolate y and get the slope-intercept form, add 3 to both sides: y = (1/2)x + 2.5, which simplifies to y = 0.5x + 2.5 if we use decimal notation. However, none of the given options matches this equation. It seems there might be an error in the point-slope form equation provided in the question, or an error in the provided answer choices.