Question

5. Find the equation of the line joining the points A(5, 7) and B(8, 12).

Answer 1

Given:

There are given that the two points:

`A(5,7),and,B(8,12)`

Step-by-step explanation:

According to the question:

We need to find the equation of the line:

Then,

To find the equation of the line, first, we need to find the slope of the line.

So,

From the formula of the slope of the line:

`m=(y_2-y_1)/(x_2-x_1)`

Where,

`x_1=5,y_1=7,x_2=8,y_2=12`

Then,

Put all the values into the given formula:

So,

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(12-7)/(8-5) \\ m=(5)/(3) \end{gathered}`

Then,

From the formula of the equation of the line:

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

Then,

Put the value of m into the above equation:

So,

`\begin{gathered} y-y_(1)=m(x-x_(1)) \\ y-7=(5)/(3)(x-5) \\ 3y-21=5(x-5) \\ 3y-21=5x-25 \end{gathered}`

Then,

`\begin{gathered} 3y-21=5x-25 \\ 3y-21+21=5x-25+21 \\ 3y=5x-4 \\ y=(5)/(3)x-(4)/(3) \end{gathered}`

Final answer:

Hence, the equation of line is shown below:

`y=(5)/(3)x-(4)/(3)`