Final answer:
To find the slope-intercept form of the line through (3, -3) and (0, -5), the slope (m) is first calculated, resulting in 2/3. This slope is then applied in the point-slope form to derive the equation y = (2/3)x - 5. None of the provided options match the correct equation, indicating a possible typo in the question or options.
Step-by-step explanation:
The student's question relates to finding the slope-intercept form of the equation of a line passing through two given points: (3, -3) and (0, -5). To start, we need to find the slope of the line using the formula slope (m) = (y2 - y1) / (x2 - x1). Plugging in the points, we get slope (m) = (-5 - (-3)) / (0 - 3) = (-2) / (-3) = 2/3. However, as we're provided with options that have an integer slope, it's clear that there might be a typo in the question as the options do not match the slope we calculated.
Nevertheless, using the slope (m), we can then use the point-slope form to find the equation of the line y - y1 = m(x - x1) and substitute either of the given points. Since a typo seems apparent, let's demonstrate the process using one of the points (3, -3) and the slope obtained from our calculation: y - (-3) = (2/3)(x - 3). This simplifies to y = (2/3)x - 2 + (-3), which becomes y = (2/3)x - 5 after combining like terms.
Unfortunately, none of the provided options match this equation, suggesting there may be a mistake in the numbers provided in the question or in the options themselves. For a correct equation based on the given points and using integer values for slope, additional information or correction would be required.