Final answer:
The equation of the line passing through the points (4,8) and (2,9) in point-slope form is y = 9 + 3x.
Step-by-step explanation:
The equation of the line passing through the points (4,8) and (2,9) in point-slope form is y = 9 + 3x.
To find the equation in point-slope form, we need to determine the slope of the line using the two given points. The slope (m) is calculated as the change in y divided by the change in x: m = (y2 - y1)/(x2 - x1). Plugging in the values, we get m = (9 - 8)/(2 - 4) = 1/-2 = -1/2.
Now that we have the slope, we can substitute one of the points and the slope into the point-slope form equation y - y1 = m(x - x1). Using the point (4,8), we have y - 8 = (-1/2)(x - 4).