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Algebra Difficulty: Hard

What is the y-coordinate of the y-intercept of the graph of $\frac{3 x}{7} = - \frac{5 y}{9} + 21$ in the xy-plane?

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Explanation

The correct answer is $StartFraction 189 Over 5 EndFraction$ . A y-intercept of a graph in the xy-plane is a point where the graph intersects the y-axis, which is a point with an x-coordinate of $0$ . Substituting $0$ for $x$ in the given equation yields $\frac{3 (0)}{7} = - \frac{5 y}{9} + 21$ , or $0 = - \frac{5 y}{9} + 21$ . Subtracting $21$ from both sides of this equation yields $- 21 = - \frac{5 y}{9}$ . Multiplying both sides of this equation by $negative 9$ yields $189 equals 5 y$ . Dividing both sides of this equation by $5$ yields $\frac{189}{5} = y$ . Therefore, the y-coordinate of the y-intercept of the graph of the given equation in the xy-plane is $StartFraction 189 Over 5 EndFraction$ . Note that 189/5 and 37.8 are examples of ways to enter a correct answer.