Question

Interpret the slope.

The balance increases $50 each week.
The balance increases $100 each week.
The balance decreases $50 each week.
The balance decreases $100 each week.

Answer 1

The slope of a line in the context of balance changes represents the rate of change per time unit. Positive slopes (50, 100) indicate an increase in balance, while negative slopes (-50, -100) indicate a decrease. The steepness of the slope corresponds to how quickly the balance changes.

Step-by-step explanation:

The question is asking for an interpretation of the slope of a line in different scenarios regarding balance changes over time. In mathematics, the slope represents the rate of change between two variables. If we have the function of a line in the form y = mx + b, where m is the slope and b is the y-intercept, then m tells us how much y changes for a one unit increase in x.

• When the balance increases by $50 each week, the slope is 50, indicating a positive increase over time.
• Similarly, if the balance increases by $100 each week, we have a slope of 100, representing a steeper positive increase.
• Conversely, a balance that decreases by $50 each week results in a slope of -50, indicating a negative trend.
• If the balance decreases by $100 each week, the slope is -100, showing a steeper negative trend.

A positive slope means the line on the graph goes upwards as we move from left to right, whereas a negative slope means the line goes downwards.