Question

question
warm-up
consider the functions shown on the graph.
select the correct answer from each drop-down menu.
line * has a negative slope.
line * has a positive slope.

Explanation:

Step1: Recall Slope Definition

The slope of a line is calculated as $\frac{\text{change in } y}{\text{change in } x}$ (rise over run). A negative slope means as $x$ increases, $y$ decreases. A positive slope means as $x$ increases, $y$ increases.

Step2: Analyze Line B

For line B, observe the graph: as $x$ values increase (move to the right), the $y$ values decrease (move down). So line B has a negative slope.

Step3: Analyze Lines with Positive Slope

For lines A and C (and check others), line A: as $x$ increases, $y$ increases (positive slope). Line C: as $x$ increases, $y$ increases (positive slope). Line D is vertical (undefined slope). So lines A or C (and B is negative) fit. Assuming the drop - down for negative slope is B, and for positive slope is A (or C, but common in such graphs A is a typical positive slope line).

Answer:

For "Line has a negative slope", the answer is Line B. For "Line has a positive slope", the answer is Line A (or Line C, depending on graph details, but Line A is a common positive - slope line here).