There are a few possible answers and they are
y - 40 = 1(x - 0)
y - 50 = 1(x - 10)
y - 60 = 1(x - 20)
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Explanation:
Pick two blue points from the graph. I recommend points that land on grid intersections so we can read the coordinates easily. Two such points are (0,40) and (10,50)
Use the slope formula to find the slope
m = (y2-y1)/(x2-x1)
m = (50-40)/(10-0)
m = 10/10
m = 1
The slope is 1.
Note how I subtracted the y coordinates, then did the same for the x coordinates in the same order, and divided the differences.
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Since your teacher wants the answer in point slope form, we'll use this as our template
y - y1 = m(x - x1)
where m is the slope and (x1,y1) a the point the line goes through. We have infinitely many choices for (x1,y1) since there are infinitely many points on this line.
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If we use (x1,y1) = (0,40), then we get
y - y1 = m(x - x1)
y - 40 = 1(x - 0)
which is one possible answer
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If we use (x1,y1) = (10,50), then we get
y - y1 = m(x - x1)
y - 50 = 1(x - 10)
which is another possible answer
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If we use (x1,y1) = (20,60), then we get
y - y1 = m(x - x1)
y - 60 = 1(x - 20)
which is another possible answer
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So again there are multiple answers possible. The slope stays the same each time, but x1 and y1 change depending on which point you choose.
