Final answer:
The equation that models the relationship between the number of pieces painted, p, and the total cost, T, is T = mp + b. The term m is the cost per piece (slope), and the term b is the initial or fixed cost (y-intercept). Option B is correct.
Step-by-step explanation:
The equation that models the relationship between the number of pieces painted, p, and the total cost, T, in the form y=mx+b, is:
T = mp + b
In this equation, m represents the slope, which indicates the cost per piece painted, and b represents the y-intercept, which corresponds to the fixed costs or the initial cost before any pieces are painted. If you were to express this equation graphically, you would find that the slope m shows how the total cost T increases for each additional piece painted p, while the y-intercept b shows the total cost when no pieces are painted (that is, where the line crosses the y-axis).
The equation in the form y=mx+b models the linear relationship between the number of pieces you paint (p) and the total cost (T). Therefore, the correct equation is:
T = mp + b
Where m represents the slope of the line and b represents the y-intercept. The slope (m) represents the rate of change or the amount the total cost changes for each additional piece painted. The y-intercept (b) represents the initial cost when no pieces are painted. By determining the values for m and b, you can accurately model the relationship between the number of pieces you paint and the total cost.