1. The problem asks to complete the grid for the relation $y = 2x - 9$ and find the values of $b$ and $d$. 2. The formula given is $y = 2x - 9$. This means for any $x$, $y$ is twice $x$ minus 9. 3. We use the table to find missing values. For $a$, $y=3$; for $b$, $y=-5$; for $c$, $y=-31$. 4. Calculate $a$ using $y=3$: $$3 = 2a - 9 \implies 2a = 12 \implies a = 6$$ 5. Calculate $b$ using $y=-5$: $$-5 = 2b - 9 \implies 2b = 4 \implies b = 2$$ 6. Calculate $c$ using $y=-31$: $$-31 = 2c - 9 \implies 2c = -22 \implies c = -11$$ 7. Now find $d$ when $x=4$: $$d = 2(4) - 9 = 8 - 9 = -1$$ 8. Check the options for $b$ and $d$: $b=2$ and $d=-1$ matches option B. Final answer: $b=2$ and $d=-1$ (Option B).