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

A line in the $xy$-plane has a slope of $\\frac{1}{9}$ and passes through the point $(0,14)$. Which equation represents this line?

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A line in the $xy$-plane has a slope of $\\frac{1}{9}$ and passes through the point $(0,14)$. Which equation represents this line?

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

Choice D is correct. The equation of a line in the $xy$-plane can be written as $y=mx+b$, where $m$ represents the slope of the line and $(0,b)$ represents the $y$-intercept of the line. It's given that the slope of the line is $\\frac{1}{9}$. It follows that $m=\\frac{1}{9}$. It's also given that the line passes through the point $(0,14)$. It follows that $b=14$. Substituting $\\frac{1}{9}$ for $m$ and $14$ for $b$ in $y=mx+b$ yields $y=\\frac{1}{9}x+14$. Thus, the equation $y=\\frac{1}{9}x+14$ represents this line.

Choice A is incorrect. This equation represents a line with a slope of $-\\frac{1}{9}$ and a $y$-intercept of $(0,-14)$.

Choice B is incorrect. This equation represents a line with a slope of $-\\frac{1}{9}$ and a $y$-intercept of $(0,14)$.

Choice C is incorrect. This equation represents a line with a slope of $\\frac{1}{9}$ and a $y$-intercept of $(0,-14)$.

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A line in the $xy$-plane has a slope of $\\frac{1}{9}$ and passes through the point $(0,14)$. Which equation represents this line?

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

$y=-\\frac{1}{9}x-14$

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

$y=-\\frac{1}{9}x+14$

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

\$y=\\frac{1}{9}x-14\$

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

$y=\\frac{1}{9}x+14$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-152"}

A line in the $xy$-plane has a slope of $\frac{1}{9}$ and passes through the point $(0,14)$. Which equation represents this line?