My problem says
The cost of a cell phone for one month is a linear function of the numbers of minutes used. The total cost for 20, 35, and 40 additional numbers Re shown.
Then it gives a table where it's 20/48$, 35/54$ and 40/56$
The first question is ,
Find the linear equation that represents the relationship between the number of additional minutes and total cost
X = Minutes used.
Y = T0tal cost in Dollars.
(X,Y), (20,48), (35,54), (40,56).
m = (Y2-Y1)/(X2-X1)=(54-48)/(35-20) =
0.40 = Slope.
(20,48)
Y = mX + b = 48
0.4*20 + b = 48
b = 40
Eq: Y = 0.4X + 40
To find the linear equation that represents the relationship between the number of additional minutes and the total cost, we can use the given values from the table.
Let's denote the number of additional minutes as x, and the total cost as y.
From the table, we have the following values:
(x, y) = (20, 48), (35, 54), (40, 56)
To find the linear equation, we need to determine the slope (m) and the y-intercept (b).
We can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points from the table to find the slope:
m = (54 - 48) / (35 - 20) = 6 / 15 = 2/5
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Let's use the first point (20, 48) to substitute the values:
y - 48 = (2/5)(x - 20)
Expanding and simplifying the equation:
y - 48 = (2/5)x - (2/5)(20)
y - 48 = (2/5)x - 8
y = (2/5)x + 40
Therefore, the linear equation that represents the relationship between the number of additional minutes (x) and the total cost (y) is:
y = (2/5)x + 40
To find the linear equation that represents the relationship between the number of additional minutes and the total cost, we need to determine the slope and the y-intercept.
In this problem, the number of additional minutes is the independent variable (x), and the total cost is the dependent variable (y).
To find the slope, we can use the formula:
slope = (change in y)/(change in x)
We can choose any two points from the table to calculate the slope. Let's choose the points (20, 48) and (35, 54).
change in y = 54 - 48 = 6
change in x = 35 - 20 = 15
slope = (6)/(15) = 0.4
Now, let's find the y-intercept. We can substitute the values of one of the points into the equation y = mx + b and solve for b.
Using the point (20, 48):
48 = 0.4(20) + b
48 = 8 + b
b = 48 - 8
b = 40
Therefore, the linear equation that represents the relationship between the number of additional minutes (x) and the total cost (y) is:
y = 0.4x + 40