Question

Suppose a 5 minute overseas call costs $5.91 and a 10 minute call costs $10.86. The cost of the call and the length of the call are related.

identify the variables in this situation
x= ?
y=?
what is the given information in this problem
y-intercept-?
slope-?
What is the cost y of a call of x minutes duration? (Assume this is a constant-increase situation)
How long can you talk on the phone if you have $12 to spend?

Answer 1

we are given the cost of an overseas call for a particular duration of time and asked to find the variables in the situation.

Since the cost of the call and its length are related,we can conclude that,

x = Length of the call (in minutes)

y = The cost of the call (in $)

Now, we can rewrite the situation in the form of y = mx + b wherein m = slope and b = y-intercept

ATQ,

y-intercept = The cost of the call which lasts for 0 minutes since there's no additional or fixed cost for the call.

slope = The rate of change of the cost wrt the duration of the call

Now, in order to find the cost (y) of a call (x) minutes duration,we can use the formula y = mx + b and in order to find m ,we can use the formula which goes by

m = (change in y)/(change in x)

here, we are given two sets or points i.e. (5.91,5) and (10.86,10)

m = (10-5)/(10.86-5.91) = 5/4.95 = 1.01

Thus, the slope of the equation is 1.01

Now, we can find the y-intercept by plugging in the value of m in the equation when y = 5.91 and x = 5

y = mx + b

5.91 = 5*1.01 + b

5.91 = 5.05 + b

b = 5.91 - 5.05

b = 0.86

thus, the y-intercept of the equation is 0.86

Now, we can find the duration of the call if we have $12 to spend

plugging in y = 12,m = 1.01 and b = 0.86

12 = 1.01x + 0.86

1.01x = 12 - 0.86

1.01x = 11.14

x = 11.14/1.01

x = 11.03 minutes

thus, if we have $12 to spend ,we can attend a call for a rough duration of 11 minutes.

Answer 2

• x: The length of the call in minutes
• y: The cost of the call in dollars
• y-intercept = 0.96
• slope = 0.99
• cost y of a call of x minutes duration:
  `\sf y = 0.99x + 0.96`
• we can talk on the phone for 11.15 minutes with $12.

Explanation:

Identifying the variables:

• x: The length of the call in minutes (independent variable)
• y: The cost of the call in dollars (dependent variable)

Given information:

• The cost of a 5-minute call is $5.91. This corresponds to the point (5, 5.91).
• The cost of a 10-minute call is $10.86. This corresponds to the point (10, 10.86).

Slope and y-intercept:

We need to determine the slope and y-intercept of the line that passes through the given points.

Slope formula:

`\sf m = \frac{{y_2 - y_1}}{{x_2 - x_1}}`

Using the given points:

`\sf m = \frac{{10.86 - 5.91}}{{10 - 5}} \\\\ = \frac{{4.95}}{{5}}\\\\ = 0.99`

Therefore, the slope of the line is 0.99.

Y-intercept formula:

We can use either point to find the y-intercept. Let's use the first point (5, 5.91):

`\sf y = mx + b`

`\sf 5.91 = 0.99 * 5 + b`

`\sf 5.91 = 4.95 + b`

`\sf b = 0.96`

Therefore, the y-intercept is 0.96.

Cost of a call of x minutes:

The equation that relates the cost (y) to the call duration (x) is:

`\sf y = 0.99x + 0.96`

This equation shows that the cost increases linearly with the duration of the call. The slope of 0.99 indicates that the cost increases by $0.99 for every additional minute of the call.

Talking time with $12:

To find how long we can talk on the phone with $12, we need to substitute
`\sf y` with 12 in the equation and solve for
`\sf x`:

`\sf 12 = 0.99x + 0.96`

`\sf 11.04 = 0.99x`

`\sf x =(11.04)/(0.99)`

`\sf x = 11.15151515`

`\sf x \approx 11.15`

Therefore, we can talk on the phone for approximately 11.15 minutes with $12.