We start by rearranging the inequality in order to have a slope-intercept version of the inequality:
[tex]\begin{gathered} y-5>2x-10 \\ y>2x-10+5 \\ y>2x-5 \end{gathered}[/tex]
We can graph the boundary line, that is y=2x-5. This line, as the sign is ">" and not ">=", does not belong to the region of the inequality.
The slope is m=2 and the y-intercept is at y=-5.
The x-intercept is at x=5/2=2.5.
We know that the region is above this line, as it comprehends the values of y that are larger that 2x-5. Remember that the sign is y > 2x-5.
Then, we can graph the inequality as:
Answer: Graph B, as the line is not included and the region of the inequality is above the line.
