Answer:
To find the slope of the line passing through the given points, we can choose any two points and calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the points (3, 6) and (-1, -4):
slope = (-4 - 6) / (-1 - 3) = -10 / -4 = 5/2
The slope of the line is 5/2.
To write an equation for the line, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Let's choose the point (3, 6) to write the equation:
y - 6 = (5/2)(x - 3)
Expanding and simplifying the equation, we get:
y - 6 = (5/2)x - 15/2
y = (5/2)x - 15/2 + 12/2
y = (5/2)x - 3/2
So, the equation of the line is y = (5/2)x - 3/2.
Now, let's check if the point (0, -2) lies on the line by substituting the coordinates into the equation:
-2 = (5/2)(0) - 3/2
-2 = 0 - 3/2
-2 = -3/2
The equation is not true, so the point (0, -2) does not lie on the line.