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Algebra / Linear functions Difficulty: Medium

In the xy-plane, the points with coordinates negative 2 comma 3 and 4 comma negative 5 lie on the graph of which of the following linear functions?

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Explanation

Choice C is correct. A linear function can be written in the form f of x  equals, m x plus b, where m is the slope and b is the y-coordinate of the y-intercept of the line. The slope of the graph can be found using the formula m equals, the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction. Substituting the values of the given points into this formula yields m equals, the fraction with numerator negative 5 minus 3, and denominator 4 minus negative 2, end fraction or m equals, negative 8 over 6, which simplifies to m equals, negative four thirds. Only choice C shows an equation with this slope.

Choices A, B, and D are incorrect and may result from computation errors or misinterpreting the given information.