Use the distance formula to determine the length of the line segment.
First, locate the two points in the graph.
We have points (-5,-2) and (2,-1).
Recall that the distance formula is in the equation.
[tex]\begin{gathered} d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \\ \text{where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the two points} \end{gathered}[/tex]Substitute and we get
[tex]\begin{gathered} (x_1,y_1)=(-5,-2) \\ (x_2,y_2)=(2,-1) \\ \\ d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \\ d = \sqrt {(2 - (-5))^2 + (-1 - (-2))^2} \\ d=\sqrt{(2+5)^2+(-1+2)^2} \\ d = \sqrt {(7)^2 + (1)^2} \\ d = \sqrt {{49} + {1}} \\ d = \sqrt {50} \\ d\approx7.071068 \end{gathered}[/tex]Rounding to the nearest tenth, the distance of the given line segment in the graph is 7.1 units.
