Final answer:
The equation of the line passing through the points (3, 4) and (-2, 9) is y = -x + 7.
Step-by-step explanation:
To find the equation of the line passing through the points (3, 4) and (-2, 9), we can use the slope-intercept form of a linear equation, which is y = mx + b. The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula m = (y2 - y1) / (x2 - x1). Using this formula, the slope of the line passing through (3, 4) and (-2, 9) is (9 - 4) / (-2 - 3) = 5 / -5 = -1.
Now that we have the slope (-1), we can choose any of the given points and substitute its coordinates into the equation y = mx + b to find the y-intercept (b). Let's use the point (3, 4): 4 = -1(3) + b. Solving for b, we get b = 7.
Therefore, the equation of the line passing through the points (3, 4) and (-2, 9) is y = -x + 7.