Question

for a linear function, which statement about slope and rate of change is true? a: Slope and rate of change are related but more information is needed to describe the relationship b: the slope is equal to the rate of change c: the slope is greater than the rate of change when the slope is positive d: there is no relationship between slope and rate of change

Answer 1

The slope of a linear function is equal to its rate of change, representing how much the dependent variable changes with respect to changes in the independent variable.

Step-by-step explanation:

For a linear function, the correct statement about slope and rate of change is: the slope is equal to the rate of change. The slope of a linear equation, usually denoted as 'm' or 'b' depending on the context, quantifies how the dependent variable changes for every one-unit increase in the independent variable. In the equation y = a + bx, 'b' represents the slope, and this numerical value directly corresponds to the average rate of change of the dependent variable 'y' with respect to the independent variable 'x'.

Understanding the relationship between slope and rate of change is critical, particularly in fields like economics where they are used to interpret the relationship between two variables. For example, a positive slope implies a direct proportional relationship between the independent and dependent variables, indicating that as one increases, the other does too.

Answer 2

Answer: b. The slope is equal to the rate of change

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Step-by-step explanation:

Consider the example equation of

y = (2/3)x + 4

The slope here is 2/3 as its to the left of the x variable.

Or you can look at the y = mx+b template

m = slope

b = y intercept

The slope tells us how to move from one point on the line to another point on the line. It also is the rate of change since

• slope = rise/run
• rise = change in y
• run = change in x

Dividing rise over run tells us how y changes with respect to x.

Going back to the example y = (2/3)x+4, a slope of 2/3 means each time x goes up by 1, y increases by 2/3.

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Another example:

A person drives 50 mph and drives for x hours

distance = rate*time

y = 50x

The 50 is the slope of the line and it is the rate of change of the car, aka the speed of the car. Each time the number of hours (x) goes up by 1, the distance (y) goes up by 50.