Question

Jay pays a flat fee each month for basic cable service. He also pays $3.50 for each movie he orders during the month. Last month, he ordered 5 movies and his total bill came to $54. Write an equation in point-slope form that represents the total bill, y, in terms of the number of movies, x. Enter your slope as a decimal without any spaces. y - = (x - )

Answer 1

Jay's total bill for cable service can be represented by the equation y = 3.50x + 36.50. To express this in point-slope form using a point on the line, such as (5, 54), the equation is y - 54 = 3.50(x - 5).

Step-by-step explanation:

To find the equation in point-slope form that represents Jay's total bill, y, in terms of the number of movies, x, we need to determine the cost per movie and the flat fee he pays monthly for basic cable service. Jay's total bill for 5 movies was $54, and since he pays $3.50 for each movie, we can calculate the flat fee.

Let's represent the flat fee by f. Since 5 movies cost $3.50 each, the total cost for the movies is 5 * $3.50 = $17.50. Now, subtracting the cost for the movies from the total bill gives us the flat fee: $54 - $17.50 = $36.50. So, f = $36.50 and the equation for the total bill can be written as y = 3.50x + 36.50, where y is the total bill and x is the number of movies ordered.

To express this in point-slope form, we choose a point that lies on the line. For example, when Jay ordered 5 movies, the total bill was $54. So, the point (5, 54) can be used. The point-slope form of an equation is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point used. The slope, or the cost per movie, is $3.50. Therefore, the equation in point-slope form is y - 54 = 3.50(x - 5).