Answer: y = (-2/3)x-5
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Step-by-step explanation:
As you probably can guess (or already know), the term "slope intercept form" means that all we need are the slope and y intercept to get the equation.
To get the slope, we need two points. Pick any two points you want. I'll pick (3,-7) and (6,-9). Notice how we go down 2 units and then over to the right 3 units when we move from the first point to the second point.
See diagram below.
So the slope is rise/run = -2/3. The negative rise indicates we go down. The run is always moving to the right. This produces the downhill trend when we move from left to right.
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We can also use the slope formula. I'll use those two points mentioned earlier.
m = (y2-y1)/(x2-x1)
m = (-9-(-7))/(6-3)
m = (-9+7)/(6-3)
m = -2/3
We get the same result as earlier
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The y intercept is where the graph crosses the vertical y axis. This is at 5. So b = 5 is the y intercept.
Since the slope is m = -2/3 and the y intercept is b = 5, we go from y = mx+b to y = (-2/3)x-5 which is our final answer.