Question

The phone company Splint has a monthly cellular plan where a customer pays a flat fee for unlimited voice calls and then a certain amount per GB of data used. If a customer uses 4 GB, the monthly cost will be $48. If the customer uses 32 GB, the monthly cost will be $160.

A) Find an equation in the form y = m x + b , where x is the number of GB of data used in a month and y is the total monthly cost of the Splint plan. Find both the Point-Slope (use first point) and the Slope Intercept form of the line:

Answer 1

The equation for the monthly cost of the Splint plan based on the amount of data used can be written in the form y = mx + b, where m is the slope and b is the y-intercept. Using the given data points, we find that the equation is y = 4x + 32.

Step-by-step explanation:

To find an equation in the form y = mx + b for the monthly cost of the Splint plan based on the amount of data used, we can use two data points: (4, $48) and (32, $160). The equation can be found using the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, we can find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get: m = (160 - 48) / (32 - 4) = 112 / 28 = 4.

Next, we can find the y-intercept (b) by plugging in one of the data points into the equation and solving for b. Using the point (4, $48), we get: $48 = 4(4) + b. Solving for b, we get: b = $48 - 16 = $32.

Therefore, the equation in the Point-Slope form is: y = 4x + 32, and the equation in the Slope-Intercept form is: y = 4x + 32.