Question

Can anyone help me i have to find a equation of the line below it's a graph can anyone help me?

Answer 1

The equation of a line given two points A and B is calculated by the formula

`\begin{gathered} A(x_1,y_1);B(x_2,y_2) \\ \text{the equation of the line AB is} \\ (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \end{gathered}`

From the graph given, we have two points.

`A(-5,3);B(5,-2)`

Substituting the values of the given points into the formula to get the equation of line

`x_1=-5;y_1=3;x_2=5;y_2=-2(\square)/(\square)`
`\begin{gathered} (y-3)/(x-(-5))=(-2-3)/(5-(-5)) \\ (y-3)/(x+4)=(-5)/(5+5) \\ (y-3)/(x+4)=-(5)/(10) \end{gathered}`
`\begin{gathered} (y-3)/(x+4)=(-1)/(2) \\ 2(y-3)=-1(x+4) \\ 2y-6=-x-4 \\ 2y+x=-4+6 \\ 2y+x=2 \end{gathered}`
`\begin{gathered} 2y=2-x \\ y=(2)/(2)-(x)/(2) \\ y=1-(x)/(2) \end{gathered}`

Hence, the equation of the line is y=1-x/2