Answer: Yes they are all on the same line.
Step-by-step explanation:
We can find an equation between two of the points and check to see if the third point is also a solution. I'll pick (1,3) and (-2,4) and calculate a slope:
y = (4-3) = 1
x = -2 - 1 = -3
slope = y/x
slope = -1/3 or -0.3333
The equation, so far, is:
y = -(1/3)x + b
We can find b by entering one of these points into the equation and solving for b. I'll pick (-2,4):
y = -(1/3)x + b
4 = -(1/3)(-2) + b
4 = (2/3) + b
b = 3 1/3 or 10/3
The equation is
y = -(1/3)x + 10/3
This equation goes through the two points we used to cacluate the slope. The third point, (4,2) can be checked to see if the equation gives us a y value of 2 if we set x=4:
y = -(1/3)x + 10/3
y = -(1/3)*(4) + 10/3
y = -(4/3) + 10/3
y = 6/3 or 2
It correctly returns a value of 2, so (4,2) is also on this line.
