Finding Points on the Line Equation 3x - 4y = 0

To determine which point lies on the graph of the line given by the equation $3x - 4y = 0$, we need to check if the coordinates of each point satisfy the equation. A point $(x, y)$ lies on the line if substituting its $x$ and $y$ values into the equation makes the equation true.

Testing the Given Points

Let's test each option:

• Option 1: (3, 4)

  Substitute $x=3$ and $y=4$ into the equation $3x - 4y = 0$: $3(3) - 4(4) = 9 - 16 = -7$ Since $-7 \neq 0$, the point (3, 4) does not lie on the line.

• Option 2: (4, 3)

  Substitute $x=4$ and $y=3$ into the equation $3x - 4y = 0$: $3(4) - 4(3) = 12 - 12 = 0$ Since $0 = 0$, the point (4, 3) satisfies the equation and lies on the line.

• Option 3: (-4, 3)

  Substitute $x=-4$ and $y=3$ into the equation $3x - 4y = 0$: $3(-4) - 4(3) = -12 - 12 = -24$ Since $-24 \neq 0$, the point (-4, 3) does not lie on the line.

Conclusion

Based on the calculations, only the point (4, 3) satisfies the equation $3x - 4y = 0$. Therefore, the graph of the line $3x - 4y = 0$ passes through the point (4, 3).