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Nonlinear equations in one variable and systems of equations in two variables SAT question

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

In the xy-plane, the graph of $y equals, x squared minus 9$ intersects line p at $the point with coordinates 1 comma a$ and $the point with coordinates 5 comma b$ , where a and b are constants. What is the slope of line p ?

ExplanationShow

Choice A is correct. It’s given that the graph of $y equals, x squared, minus 9$ and line p intersect at $the point with coordinates 1 comma a$ and $the point with coordinates 5 comma b$ . Therefore, the value of y when $x equals 1$ is the value of a, and the value of y when $x equals 5$ is the value of b. Substituting 1 for x in the given equation yields $y equals, 1 squared minus 9$ , or $y equals negative 8$ . Similarly, substituting 5 for x in the given equation yields $y equals, 5 squared minus 9$ , or $y equals 16$ . Therefore, the intersection points are $the point with coordinates 1 comma negative 8$ and $the point with coordinates 5 comma 16$ . The slope of line p is the ratio of the change in y to the change in x between these two points: $the fraction with numerator 16 minus negative 8, and denominator 5 minus 1, end fraction, equals the fraction 24 over 4$ , or 6.

Choices B, C, and D are incorrect and may result from conceptual or calculation errors in determining the values of a, b, or the slope of line p.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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