Question

Which graph represents the linear function y = start fraction 1 over 5 end fractionx – 2?
A. A line on a graph passes through the points left-parenthesis negative 5 comma negative 1 right-parenthesis left-parenthesis zero comma negative 2 right-parenthesis left-parenthesis 5 comma negative 3 right-parenthesis.
B. A line on a graph passes through the points left-parenthesis negative 5 comma negative 3 right-parenthesis left-parenthesis zero comma negative 2 right-parenthesis left-parenthesis 5 comma negative 1 right-parenthesis.
C. A line on a graph passes through the points left-parenthesis zero comma negative 2 right-parenthesis and left-parenthesis 1 comma 3 right-parenthesis.
D. A line on a graph passes through the points left-parenthesis negative 5 comma 1 right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 5 comma 3 right-parenthesis.

Answer 1

The correct answer is B. A linear function has a constant rate of change, which in this case is a slope of 1/5. The y-intercept is -2, meaning the line crosses the y-axis at -2. By looking at the points provided in option B, we can see that they all lie on the line y = (1/5)x - 2, so it represents the linear function in the question.