Write the equation of the line passing through points (3, -2) and (6, 4).

the slope is (4+2)/(6-3) = 2, so

y-4 = 2(x-6)

To write the equation of a line, you can use the slope-intercept form, which is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope (m) of the line passing through two points (x1, y1) and (x2, y2), use the formula:

m = (y2 - y1) / (x2 - x1)

Let's calculate the slope first:

m = (4 - (-2)) / (6 - 3)
m = 6 / 3
m = 2

Now, substitute one of the points and the slope into the equation y = mx + b to find the y-intercept (b). You can choose either point (3, -2) or (6, 4). Let's use the point (3, -2):

-2 = 2(3) + b
-2 = 6 + b

Finally, solve for b:

b = -2 - 6
b = -8

Now, we have the slope (m = 2) and the y-intercept (b = -8). Plug these values back into the slope-intercept form of the equation to get the final answer:

y = 2x - 8

Therefore, the equation of the line passing through the points (3, -2) and (6, 4) is y = 2x - 8.