State whether the following statement is true or false:
The graph of the linear equation $5x - 3y = 30$ intersects the $y$-axis at the point $(6, 0)$.
The graph of the linear equation $5x - 3y = 30$ intersects the $y$-axis at the point $(6, 0)$.
(B) The statement is False.
To find the intersection point with the $y$-axis,we set $x = 0$ in the equation $5x - 3y = 30$.
Substituting $x = 0$: $5(0) - 3y = 30 \implies -3y = 30 \implies y = -10$.
Thus,the graph intersects the $y$-axis at the point $(0, -10)$.
Conversely,if we check the point $(6, 0)$ by substituting $x = 6$ and $y = 0$ into the equation: $5(6) - 3(0) = 30 - 0 = 30$. This point lies on the $x$-axis,not the $y$-axis.
To find the intersection point with the $y$-axis,we set $x = 0$ in the equation $5x - 3y = 30$.
Substituting $x = 0$: $5(0) - 3y = 30 \implies -3y = 30 \implies y = -10$.
Thus,the graph intersects the $y$-axis at the point $(0, -10)$.
Conversely,if we check the point $(6, 0)$ by substituting $x = 6$ and $y = 0$ into the equation: $5(6) - 3(0) = 30 - 0 = 30$. This point lies on the $x$-axis,not the $y$-axis.
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