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Algebra / Linear functions Difficulty: Easy

The graph of the function f is a line in the xy-plane. If the line has slope $three-fourths$ and $f of 0, equals 3$ , which of the following defines f?

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Explanation

Choice B is correct. The equation for the function f in the xy-plane can be represented by $f of x equals, m x plus b$ , where m is the slope and b is the y-coordinate of the y-intercept. Since it’s given that the line has a slope of $three fourths$ , it follows that $m equals three fourths$ in $f of x equals, m x plus b$ , which yields $y equals, three fourths x, plus b$ . It’s given that $f of 0 equals 3$ . This implies that the graph of the function f in the xy-plane passes through the point $with coordinates 0 comma 3$ . Thus, the y-coordinate of the y-intercept of the graph is 3, so $b equals 3$ in $f of x equals, three fourths x, plus b$ , which yields $f of x equals, three fourths x, plus 3$ . Therefore, the equation $f of x equals, three fourths x, plus 3$ defines the function f.

Choice A is incorrect and may result from a sign error for the y-intercept. Choice C is incorrect and may result from using the denominator of the given slope as m in $f of x equals, m x plus b$ , in addition to a sign error for the y-intercept. Choice D is incorrect and may result from using the denominator of the given slope as m in $f of x equals, m x plus b$ .