Given:
There are given that the two points:
[tex]A(5,7),and,B(8,12)[/tex]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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=5,y_1=7,x_2=8,y_2=12[/tex]Then,
Put all the values into the given formula:
So,
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{12-7}{8-5} \\ m=\frac{5}{3} \end{gathered}[/tex]Then,
From the formula of the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]Then,
Put the value of m into the above equation:
So,
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-7=\frac{5}{3}(x-5) \\ 3y-21=5(x-5) \\ 3y-21=5x-25 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3y-21=5x-25 \\ 3y-21+21=5x-25+21 \\ 3y=5x-4 \\ y=\frac{5}{3}x-\frac{4}{3} \end{gathered}[/tex]Final answer:
Hence, the equation of line is shown below:
[tex]y=\frac{5}{3}x-\frac{4}{3}[/tex]