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