Final answer:
The equation of the line that passes through the points –(3, 7) and (9, –1) is y = (–2/3)x + 5, derived by calculating the slope and then using the point-slope form to find the equation.
Step-by-step explanation:
The student is asking for the equation of a line that passes through two given points, –(3, 7) and (9, –1). To find this equation, we first need to calculate the slope of the line. The slope (m) is found by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting our points, we get m = (–1 – 7) / (9 – (–3)) = –8 / 12 = –2/3. With the slope and one point, we can use the point-slope form of a line, which is y - y1 = m(x - x1), and plug in the values. Using point (–3, 7), the equation becomes y – 7 = (–2/3)(x – (–3)). To write this in slope-intercept form (y = mx + b), we simplify to get the final equation: y = (–2/3)x + 5. Therefore, the equation of the line passing through the points (–3, 7) and (9, –1) is y = (–2/3)x + 5.