1. **State the problem:** Determine whether each given point lies on the specified line by substituting the point's coordinates into the line's equation and checking if the equation holds true. 2. **Recall the rule:** A point $(x_0,y_0)$ lies on the line defined by an equation if substituting $x=x_0$ and $y=y_0$ satisfies the equation. 3. **Solve each part:** **a.** Check if $(3,0)$ lies on $y=3x$. Substitute $x=3$, $y=0$: $$0 \stackrel{?}{=} 3 \times 3 = 9$$ False. **b.** Check if $(1,-6)$ lies on $y = x - 7$. Substitute $x=1$, $y=-6$: $$-6 \stackrel{?}{=} 1 - 7 = -6$$ True. **c.** Check if $(1,4)$ lies on $x + 2y = 9$. Substitute $x=1$, $y=4$: $$1 + 2 \times 4 = 1 + 8 = 9$$ True. **d.** Check if $(0,0)$ lies on $2x - 3y = 0$. Substitute $x=0$, $y=0$: $$2 \times 0 - 3 \times 0 = 0$$ True. **e.** Check if $(1,-1)$ lies on $4x - y + 1 = 0$. Substitute $x=1$, $y=-1$: $$4 \times 1 - (-1) + 1 = 4 + 1 + 1 = 6 \neq 0$$ False. **f.** Check if $(2,0)$ lies on $3x - 4y + 1 = 0$. Substitute $x=2$, $y=0$: $$3 \times 2 - 4 \times 0 + 1 = 6 + 0 + 1 = 7 \neq 0$$ False. 4. **Summary:** - a: False - b: True - c: True - d: True - e: False - f: False This method ensures you verify each point by direct substitution and comparison.