Final answer:
The slope-intercept form of the equation of the line passing through (3, -3) and (0, -5) is calculated by first determining the slope (m) and then using the point-slope form to arrange it into the slope-intercept form y = 2/3x - 5.
Step-by-step explanation:
To write the slope-intercept form of the equation of the line through the points (3, -3) and (0, -5), we first calculate the slope (m) using these points. The slope is determined by the formula m = (y2 - y1) / (x2 - x1). Plugging in the points gives us m = (-5 - (-3)) / (0 - 3) = -2 / -3, which simplifies to 2/3. Now that we have the slope, we can use the point-slope form y - y1 = m(x - x1) and plug in one of the points and the slope. Let's use the point (3, -3): y - (-3) = 2/3(x - 3).
Expanding this, we get y + 3 = 2/3x - 2. To put it in slope-intercept form (y = mx + b), we subtract 3 from both sides to get the final equation: y = 2/3x - 5. This is the equation in slope-intercept form where m is the slope and b is the y-intercept.