Question

a car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. during week 2 of the recall, the manufacturer fixed 192 cars. in week 4, manufacturer fixed 184 cars. assume that the reduction in the number of cars each week is linear. write an equation in function form to show the number of cars seen each week at the mechanic.

a f(x)=4x + 200

b f(x)=2x + 192

c f(x)=-4x + 200

d f(x)=-2x + 192

question 11 (1 point)
(02.03 mc)
a telephone company charges a fixed monthly rate plus a rate per megabyte of data used. the company charges $120 for 100 megabytes of data and $95 for 50 megabytes of data. an equation can be written to show the relationship between the total megabytes of data used (x) and the total monthly charges (y). which of the following best describes the steps to draw the graph?

a draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 0.50

b draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 2

c draw a graph that joins the points (120, 100) and (95, 50) and has a slope = 2

d draw a graph that joins the points (120, 100) and (95, 50) and has a slope = 0.50

Explanation:

For the first problem about the car - recall:

Step1: Identify two points

Let \(x\) be the week number and \(y = f(x)\) be the number of cars fixed. We have the points \((2,192)\) and \((4,184)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 2,y_1=192,x_2 = 4,y_2 = 184\), we get \(m=\frac{184 - 192}{4 - 2}=\frac{-8}{2}=-4\).

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((2,192)\) and \(m=-4\), we have \(y-192=-4(x - 2)\).

Step4: Simplify the equation

\[

$$\begin{align*} y-192&=-4x + 8\\ y&=-4x+200 \end{align*}$$

\]

Step1: Identify the two points

The points are \((x_1,y_1)=(50,95)\) and \((x_2,y_2)=(100,120)\) where \(x\) is the number of megabytes and \(y\) is the total monthly charge.

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values, we get \(m=\frac{120 - 95}{100 - 50}=\frac{25}{50}=0.5\).
The graph of the linear relationship between the total megabytes of data used (\(x\)) and the total monthly charges (\(y\)) passes through the points \((50,95)\) and \((100,120)\) with a slope of \(0.5\).

Answer:

C. \(f(x)=-4x + 200\)

For the second problem about the telephone company charges: