By your cell phone contract, you pay a monthly fee plus some money for each minute you use the phone during the month. In one month, you spent 200 minutes on the phone, and paid $22.45. In another month, you spent 350 minutes on the phone, and paid $29.65.
Let x be the number of minutes you talk over the phone in a month, and let y be your cell phone bill for that month. Use a linear equation to model your monthly bill based on the number of minutes you talk over the phone.
1. This linear model’s slope-intercept equation is?
2. If you spent 110 minutes over the phone in a month, you would pay how much?
3. If in a month, you paid $34.10
of cell phone bill, you must have spent how many minutes on the phone in that month?
1. Let's use the formula y = mx + b, where x represents the number of minutes and y represents the cell phone bill. We can solve for m (the slope) and b (the y-intercept) using the given information.
First, let's calculate the slope (m). We have two data points: (200, $22.45) and (350, $29.65). We can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = ($29.65 - $22.45) / (350 - 200)
m = $7.20 / 150
m = 0.048
The slope (m) is 0.048.
Next, let's calculate the y-intercept (b). We can use one of the data points with the formula y = mx + b. Let's use (200, $22.45):
$22.45 = (0.048)(200) + b
$22.45 = 9.6 + b
b = $22.45 - $9.6
b = $12.85
The y-intercept (b) is $12.85.
Therefore, the slope-intercept equation for the monthly bill is y = 0.048x + $12.85.
2. To find out how much you would pay if you spent 110 minutes on the phone, we substitute x = 110 into the equation:
y = 0.048(110) + $12.85
y = $5.28 + $12.85
y = $18.13
If you spent 110 minutes on the phone, you would pay $18.13.
3. To determine how many minutes you spent on the phone if you paid $34.10, we set y = $34.10 in the equation and solve for x:
$34.10 = 0.048x + $12.85
$34.10 - $12.85 = 0.048x
$21.25 = 0.048x
x = $21.25 / 0.048
x ≈ 442.71
If you paid $34.10 for the cell phone bill, you must have spent approximately 443 minutes on the phone in that month.
1. To find the slope-intercept equation of the linear model, we can first find the slope (m) and the y-intercept (b).
Let's use the information from the two given data points:
Data Point 1: (200 minutes, $22.45)
Data Point 2: (350 minutes, $29.65)
We can use the formula for slope (m):
m = (y2 - y1) / (x2 - x1)
Using the values from the data points:
m = ($29.65 - $22.45) / (350 minutes - 200 minutes)
m = $7.20 / 150 minutes
m = 0.048
Now, we can substitute the slope (m) and one of the data points (200 minutes, $22.45) into the slope-intercept form equation:
y = mx + b
$22.45 = 0.048 * 200 minutes + b
Simplifying and solving for b:
$22.45 = 9.6 + b
b = $22.45 - $9.6
b = $12.85
Therefore, the slope-intercept equation is y = 0.048x + 12.85.
2. If you spent 110 minutes over the phone in a month, we can substitute x = 110 into the equation and solve for y:
y = 0.048 * 110 + 12.85
y = $5.28 + $12.85
y = $18.13
So, you would pay $18.13 if you spent 110 minutes on the phone in a month.
3. If you paid $34.10 for your cell phone bill in a month, we can substitute y = $34.10 into the equation and solve for x:
$34.10 = 0.048x + 12.85
0.048x = $34.10 - $12.85
0.048x = $21.25
x = $21.25 / 0.048
Calculating this value:
x ≈ 442.71
Therefore, you must have spent approximately 443 minutes on the phone in a month if your cell phone bill was $34.10.
To find the slope-intercept equation, we need to determine the slope and the y-intercept.
1. To find the slope, we can use the formula:
slope = (change in y) / (change in x)
Let's choose the first set of data: (x1, y1) = (200, $22.45) and (x2, y2) = (350, $29.65)
slope = (29.65 - 22.45) / (350 - 200)
= 7.20 / 150
= 0.048
So, the slope is 0.048.
2. Now, let's find the y-intercept. We can pick any of the data points to calculate it. Let's use (x1, y1) = (200, $22.45).
We can use the slope-intercept form of a linear equation:
y = mx + b
Plugging in the values: 22.45 = (0.048)(200) + b
Solving for b: b = 22.45 - 9.6
b = 12.85
So, the y-intercept is 12.85.
3. Now that we have the slope and the y-intercept, we can write the linear model's slope-intercept equation:
y = 0.048x + 12.85
Therefore, the linear model's slope-intercept equation is y = 0.048x + 12.85.
To answer the other questions:
2. If you spent 110 minutes over the phone in a month, substitute x = 110 into the equation:
y = 0.048(110) + 12.85
y = 5.28 + 12.85
y ≈ $18.13
So, if you spent 110 minutes on the phone, you would pay approximately $18.13.
3. If in a month, you paid $34.10 for cell phone bill, substitute y = $34.10 into the equation:
$34.10 = 0.048x + 12.85
0.048x = $34.10 - $12.85
0.048x = $21.25
x = $21.25 / 0.048
x ≈ 443.75
So, if you paid $34.10 for your cell phone bill, you must have spent approximately 443.75 minutes on the phone that month.
1. Y = Co + C*x.
22.45 = Co + C*200,
Co = 22.45 - 200C.
29.65 = Co + C*350.
Co = 29.65 - 350C. = 22.45 - 200C
150C = 7.20, C = 0.048/min.
Co = 22.45 - 200*0.048 = $12.85/mo. = Initial cost.
Y = 0.048x + 12.85.
2. Y = 0.048*110 + 12.85 = $18.13.
3. 34.10 = 0.048x + 12.85, X = ?.