Question

How do I write a formula that expresses y in terms of x

Answer 1

The Solution:

Given the points:

`(-1.2,2.1)\text{ and (3.5,11.03)}`

Part a:

The rate of change of y with respect to x can be calculated with the formula below:

`\text{ rate of change =}(y_2-y_1)/(x_2-x_1)`

Where,

`\begin{gathered} x_1=-1.2 \\ y_1=2.1 \\ x_2=3.5 \\ y_2=11.03 \end{gathered}`

Putting these values in the formula, we get

`\text{ rate of change in y =}(11.03-2.1)/(3.5--1.2)=(8.93)/(3.5+1.2)=(8.93)/(4.7)=(19)/(10)=1.9`

Part B:

To write the formula that expresses y in terms of x.

We shall use the formula for the equation of a line:

`y-y_1=m(x-x_1)`

Where,

m = rate of change in y = slope = 1.9

`\begin{gathered} x_1=-1.2 \\ y_1=2.1 \end{gathered}`

Substituting these values in the above formula, we get

`\begin{gathered} y-2.1=1.9(x--1.2) \\ \\ y-2.1=1.9(x+1.2) \end{gathered}`

Clearing the bracket, we get

`\begin{gathered} y-2.1=1.9x+2.28 \\ \\ y=1.9x+2.28+2.1 \\ \\ y=1.9x+4.38 \end{gathered}`

Thus, the answer to part B is:

`y=1.9x+4.38`

Part C:

To find the value of y when x=114

We shall substitute 114 for x in the equation.

`y=1.9(114)+4.38=216.6+4.38=220.98`

Thus, the correct answer is: y = 220.98