Final answer:
Whether a relation is a function can be determined by using the vertical line test. Straight lines, whether with positive, negative, or zero slope, are functions because they pass the vertical line test, meaning each x-value has one unique y-value.
Step-by-step explanation:
A student has asked if the relation is a function, and the answer to this question depends on whether the graph of the relation passes the vertical line test. If a vertical line intersects the graph at more than one point, the graph does not represent a function. This is because, by definition, for each value of the independent variable (x), there must be only one corresponding value of the dependent variable (y) in a function.
In the provided options, the lines described by a straight line with a negative slope, a straight line with a positive slope, a horizontal line at a negative value, and a horizontal line at a positive value (linear equations), all would pass the vertical line test. They represent functions as their graphs would be straight lines which would mean each x-value has only one y-value. The equations of these lines are in the form y = mx + b or y = a + bx, where m or b represent the slope, and a represents the y-intercept.