Answer: y = -2x+7
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First find the slope
m = (y2-y1)/(x2-x1)
m = (-7-1)/(7-3)
m = -8/4
m = -2
The slope is -2.
Now pick either point for the (x,y) coordinate values. I'll pick the first point. So (x,y) = (3,1)
We'll plug m = -2, x = 3, y = 1 into the equation below to solve for b
y = mx+b
1 = -2*3+b
1 = -6+b
1+6 = b ... add 6 to both sides
7 = b
b = 7
The y intercept is 7.
Since m = -2 and b = 7, we go from y = mx+b to y = -2x+7
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As a check:
Plug in (x,y) = (3,1)
y = -2x+7
1 = -2(3)+7
1 = -6+7
1 = 1
So (3,1) is confirmed.
Let's check the other point
y = -2x+7
-7 = -2(7)+7
-7 = -14+7
-7 = -7
The other point (7,-7) is confirmed as well. Both points are on the line. This confirms the answer.