Question

the solution set of $5x + 2y \leq 10$ is graphed on a coordinate plane. complete each statement about the graph so that they are true.\
the test point $(0, 0)$ \\u200bselect choice \\u200b a solution of the inequality, so the half - plane that \\u200bselect choice \\u200b contain this point will be shaded\
the boundary will be a \\u200bselect choice \\u200b line through $(0, \\u200bselect choice \\u200b)$ and $(\\u200bselect choice \\u200b, 0)$

Explanation:

Step1: Test the point (0,0) in the inequality

Substitute \( x = 0 \) and \( y = 0 \) into \( 5x + 2y \leq 10 \).
\( 5(0)+2(0)=0 \leq 10 \), which is true. So (0,0) is a solution, and the half - plane containing (0,0) will be shaded.

Step2: Find the boundary line equation

The inequality is \( 5x + 2y \leq 10 \). The boundary line is \( 5x+2y = 10 \). To find the y - intercept, set \( x = 0 \): \( 5(0)+2y=10\Rightarrow y = 5 \). To find the x - intercept, set \( y = 0 \): \( 5x+2(0)=10\Rightarrow x = 2 \). So the boundary line is a line through (0, 5) and (2, 0), and since the inequality is \( \leq \), the boundary line is solid.

Answer:

• The test point (0, 0) is a solution of the inequality, so the half - plane that contains this point will be shaded.
• The boundary will be a solid line through (0, 5) and (2, 0)