Ann started her own grocery-delivery service. The amount of money she charges for a delivery depends on the total price of the groceries. Ann uses a function of the form f(x)=mx+b, where m and b are constants, to determine the delivery fee for groceries that cost x dollars. This table shows two values of the function.x f(x)50 1675 19Find an expression for f(x). Write your answer in the form f(x)=mx+b, where m and b are integers or decimals. Do not round.
Question
Ann started her own grocery-delivery service. The amount of money she charges for a delivery depends on the total price of the groceries. Ann uses a function of the form f(x)=mx+b, where m and b are constants, to determine the delivery fee for groceries that cost x dollars. This table shows two values of the function.x f(x)50 1675 19Find an expression for f(x). Write your answer in the form f(x)=mx+b, where m and b are integers or decimals. Do not round.
Solution
To find the expression for f(x), we first need to determine the values of m (the slope) and b (the y-intercept).
The slope m can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, we can use the points (50, 16) and (75, 19) from the table.
So, m = (19 - 16) / (75 - 50) = 3 / 25 = 0.12.
Next, we find the y-intercept b using the formula b = y - mx, where (x, y) is a point on the line. We can use the point (50, 16).
So, b = 16 - 0.12 * 50 = 16 - 6 = 10.
Therefore, the expression for f(x) is f(x) = 0.12x + 10.
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