Question

a measurement of 2 inches is equalivant to 5.08 centimeters. a measurement of 5 inches is equalivant to 12.70 centimeters. write an equation to convert inches too centimeters. a) y=0.394x b) y=2.54xc) y=7.62xd) y=2x+5.08

Answer 1

Step-by-step explanation

We must find an equation that converts inches to centimeters. This means that the inputs of the equation (i.e. the x-values) must be inches whereas its outputs (i.e. its y-values) must be centimeters. Then if we have a certain number of inches x and its equivalent in centimeters is y then the equation that converts inches to centimeters defines a line that passes through all points of the form (x,y).

We know that 2 inches is equivalent to 5.08 centimeters and that 5 inches is equalivant to 12.70 centimeters. Then we have the following two points (2,5.08) and (5,12.70) which are part of the line defined by the equation that converts inches to centimeters. This equation in slope intercept form looks like this:

`y=mx+b`

From the first point we have x=2 and y=5.08 and for the second we have x=5 and y=12.70. With these two pairs of (x,y) values we can construct two equations that will allow us to find m and b and consequently the conversion equation. Then we get:

`\begin{gathered} 5.08=2m+b \\ 12.70=5m+b \end{gathered}`

We substract 2m from both sides of the first equation:

`\begin{gathered} 5.08-2m=2m+b-2m \\ b=5.08-2m \end{gathered}`

Now we replace b with this expression in the second equation:

`\begin{gathered} 12.70=5m+b=5m+5.08-2m \\ 12.70=3m+5.08 \end{gathered}`

We substract 5.08 from both sides:

`\begin{gathered} 12.70-5.08=3m+5.08-5.08 \\ 7.62=3m \end{gathered}`

And we divide both sides by 3:

`\begin{gathered} (7.62)/(3)=(3m)/(3) \\ m=2.54 \end{gathered}`

Now we use this value in the expression for b that we found before:

`\begin{gathered} b=5.08-2m=5.08-2\cdot2.54 \\ b=5.08-5.08 \\ b=0 \end{gathered}`

Then the equation that we are looking for is:

`y=2.54x`Answer

Then the answer is option b.