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

$x$	$y$
1	5
2	7
3	9
4	11

The table above shows some pairs of $x$ values and $y$ values. Which of the following equations could represent the relationship between $x$ and $y$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-154"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$x$	$y$
1	5
2	7
3	9
4	11

The table above shows some pairs of $x$ values and $y$ values. Which of the following equations could represent the relationship between $x$ and $y$?

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

Choice A is correct. Each of the choices is a linear equation in the form $y=mx+b$, where $m$ and $b$ are constants. In this equation, $m$ represents the change in $y$ for each increase in $x$ by $1$. From the table, it can be determined that the value of $y$ increases by $2$ for each increase in $x$ by $1$. In other words, for the pairs of $x$ and $y$ in the given table, $m=2$ . The value of $b$ can be found by substituting the values of $x$ and $y$ from any row of the table and substituting the value of $m$ into the equation $y=mx+b$ and then solving for $b$. For example, using $x = 1$, $y = 5$, and $m = 2$ yields $5 = 2(1)+ b$. Solving for $b$ yields $b = 3$. Therefore, the equation $y = 2x + 3$ could represent the relationship between $x$ and $y$ in the given table.

Alternatively, if an equation represents the relationship between $x$ and $y$, then when each pair of $x$ and $y$ from the table is substituted into the equation, the result will be a true statement. Of the equations given, the equation $y = 2x+ 3$ in choice A is the only equation that results in a true statement when each of the pairs of $x$ and $y$ are substituted into the equation.

Choices B, C, and D are incorrect because when at least one pair of $x$ and $y$ from the table is substituted into the equations given in these choices, the result is a false statement. For example, when the pair $x = 4$ and $y = 11$ is substituted into the equation in choice B, the result is $11 = 3(4) – 2$, or $11 = 10$, which is false.

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

$x$	$y$
1	5
2	7
3	9
4	11

The table above shows some pairs of $x$ values and $y$ values. Which of the following equations could represent the relationship between $x$ and $y$?

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

$y=3x-2$

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

$y=4x-1$

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

$y=5x$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$y=2x+3$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-154"}