What is the linear function in the form y=mx+b for the line passing through (4.5, negative 4.25 ) with a y-intercept of 2.5

Use the slope-intercept form y = mx + b.  You are given b=2.5 and are told that in one case, y = -4.25 and x = 4.5.

Then    y = mx + b   becomes   -4.25 = m(4.5) + 2.5

Multiply all 3 terms by 100:  -425 = m(450) + 250.  Subtract 250 from both sides.   The result is   -175 = m(450).   Solving for m, 

m = -175 / 450 = -7/18

Then the equation is    y = (-7/18)x + 2.5

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