{"@context":"https://schema.org/","@type":"Quiz","name":"

The graph of $7x+2y=-31$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $ \\frac{b}{a} $?

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The graph of $7x+2y=-31$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $ \\frac{b}{a} $?

","comment":{"@type":"Comment","text":"

Choice D is correct. The $x$-coordinate $a$ of the $x$-intercept $(a,0)$ can be found by substituting $0$ for $y$ in the given equation, which gives $7x+2(0)=-31$, or $7x=-31$. Dividing both sides of this equation by $7$ yields $x=-\\frac{31}{7}$. Therefore, the value of $a$ is $ -\\frac{31}{7}$. The $y$-coordinate $b$ of the $y$-intercept $(0,b)$ can be found by substituting $0$ for $x$ in the given equation, which gives $7(0)+2y=-31$, or $2y=-31$. Dividing both sides of this equation by $2$ yields $y=-\\frac{31}{2}$. Therefore, the value of $b$ is $ -\\frac{31}{2}$. It follows that the value of $ \\frac{b}{a} $ is $ \\frac{-\\frac{31}{2}}{-\\frac{31}{7}} $, which is equivalent to $ \\left(\\frac{31}{2}\\right)\\left(\\frac{7}{31}\\right) $, or $ \\frac{7}{2} $.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

"},"encodingFormat":"text/markdown","text":"

The graph of $7x+2y=-31$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $ \\frac{b}{a} $?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$ -\\frac{7}{2} $

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$ -\\frac{2}{7} $

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$ \\frac{2}{7} $

"}],"acceptedAnswer":{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$ \\frac{7}{2} $

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-91"}

The graph of $7x+2y=-31$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $ \frac{b}{a} $?