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Linear equations in two variables SAT question

Math · Algebra · Hard · Answer it here, explanation included.

The graph of the equation $a, x plus k y, equals 6$ is a line in the xy-plane, where a and k are constants. If the line contains the points $with coordinates negative 2 comma negative 6$ and $0 comma negative 3$ , what is the value of k ?

ExplanationShow

Choice A is correct. The value of k can be found using the slope-intercept form of a linear equation, $y equals, m x plus b$ , where m is the slope and b is the y-coordinate of the y-intercept. The equation $a, x plus, k y equals 6$ can be rewritten in the form $y equals, the negative of the fraction a, x, over k, end fraction, plus, the fraction 6 over k$ . One of the given points, $with coordinates 0 comma negative 3$ , is the y-intercept. Thus, the y-coordinate of the y-intercept $negative 3$ must be equal to $the fraction 6 over k$ . Multiplying both sides by k gives $negative 3 k, equals 6$ . Dividing both sides by $negative 3$ gives $k equals negative 2$ .

Choices B, C, and D are incorrect and may result from errors made rewriting the given equation.

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Linear equations in two variables SAT question

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