Question

A line passes through the points (2,18) and (7,23). Write a linear function rule in terms of x and y forthis line.The linear function rule is y=[

Answer 1

Answer::

`y=x+16`

Explanation:

Given two points on a line:

`\begin{gathered} (x_1,y_1)=(2,18) \\ \left(x_2,y_2\right)=\left(7,23\right) \end{gathered}`

We use the two-point formula below to find the linear function rule.

`$$(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)$$`

Substitute the values:

`\begin{gathered} (y-18)/(x-2)=(23-18)/(7-2) \\ (y-18)/(x-2)=(5)/(5) \\ (y-18)/(x-2)=1 \end{gathered}`

Next, make y the subject:

`\begin{gathered} y-18=x-2 \\ y=x-2+18 \\ y=x+16 \end{gathered}`

The linear function rule is:

`y=x+16`