Question

Enter the equation of the line in the given form.

Answer 1

To solve the exercise you can use the point-slope formula, that is,

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}`

So, in this case, you have

`\begin{gathered} m=(5)/(7) \\ (x_1,y_1)=(-2,5) \end{gathered}`
`\begin{gathered} y-y_1=m(x-x_1) \\ y-5=(5)/(7)(x-(-2)) \\ y-5=(5)/(7)(x+2) \\ y-5=(5)/(7)x+(10)/(7) \\ \text{ Add 5 to both sides of the equation} \\ y-5+5=(5)/(7)x+(10)/(7)+5 \\ y=(5)/(7)x+(45)/(7) \end{gathered}`

Therefore, the equation of the line in its point-slope form for this exercise is

`y=(5)/(7)x+(45)/(7)`