Question

which key feature do the graph, table, and equation have in common?

x	y
0	-0.5
5	-10.5

$-x + 2y = 6$

\\(\bigcirc\\) y - intercept

\\(\bigcirc\\) they do not have any of these features in common.

\\(\bigcirc\\) slope

\\(\bigcirc\\) x - intercept

Explanation:

Step1: Find graph's key features

• Slope: Using points (2,0) and (0,-3), slope $m=\frac{0-(-3)}{2-0}=\frac{3}{2}$
• y-intercept: $(0, -3)$
• x-intercept: $(2, 0)$

Step2: Find table's key features

• Slope: $m=\frac{-0.5-9.5}{0-(-5)}=\frac{-10}{5}=-2$
• y-intercept: $(0, -0.5)$
• x-intercept: Solve $y=0$: $0=-2x-0.5 \implies x=-0.25$

Step3: Find equation's key features

Rewrite $-x+2y=6$ as $y=\frac{1}{2}x+3$

• Slope: $m=\frac{1}{2}$
• y-intercept: $(0, 3)$
• x-intercept: Set $y=0$: $0=\frac{1}{2}x+3 \implies x=-6$

Step4: Compare all features

No matching slope, y-intercept, or x-intercept across all three.

Answer:

They do not have any of these features in common.