Answer:
The slope of the line formed by the given points is -(1/3)
Explanation:
We can find the slope in either of two ways: Graphing or Mathematically. We'll try both.
Graphing
See the attached graph. Plot the given points and then enter a line equation in the form of y=mx+b with a guess at the slope, m, and the y-intercept, b. We can see that the line angles downward to the right, so it has a negative slope. We can also see that the drop in y for every 1 increase in x only has a small impact. As x goes from 0 to 9, y drops and only by 3. That suggests a slope of (-3/9). Let's try using -(1/3) as the slope, m. And we can see from the graph that the line intersect the y axis at 0 when x = 0. So the value of the y-intercept (b) must be 0. That would suggest an equation of y = -(1/3)x+0 should work. Add that line to the plot and one can see that it does fit all the points. The line is correct and we conclude that the slope of -(1/3) is confirmed.
Mathematically
The slope of a line is also called the Rise/Run, the change in x based on a change in y. Lets pick any two points and calculate these values. I'll pick (-9,3) and (0,0). For a straight line, any tweo points will work. They will all give the same answer for the slope. I picked these two mostly because (0,0) holds a lot of promise for making life easier.
Going from (-9.3) to (0,0):
Rise is the change in x: (0 - (-9)) = 9
Run is the change in y for the same points: (0 - 3) = -3
Rise/Run is the slope (m) = (9/-3) or -(1/3)
We can now use -(1/3) in place of m in y=mx+b:
y = -(1/3)x + b
To find b, use any of the given points and solve for b. I'll use (9,-3):
y = -(1/3)x + b
-3 = -(1/3)(9) + b for (9,-3)
-3 = -3 + b
b = 0
The equation of the line formed by these points is y = -(1/3)x