Given the linear function:
What is the rate of change of the function?
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Given the linear function:
What is the rate of change of the function?
The given linear function is . This can be rearranged to fit the standard format of a linear equation, , as .
In this form, the slope is simply the coefficient of . Here, .
The slope of the linear function represents the rate of change of the function with respect to , meaning for every unit increase in , the value of decreases by 4 units.
Therefore, the rate of change of the function is , which is option 4 among the given choices.
Thus, the solution to the problem is .
What is the solution to the following inequality?
\( 10x-4≤-3x-8 \)
Rate of change is how much y changes when x increases by 1 unit. In , the slope m is always the rate of change.
A negative rate of change means the function is decreasing. As x gets larger, y gets smaller. The line slopes downward from left to right.
Move the x term first: becomes . Now you can easily see the slope is -4.
It means for every 1 unit increase in x, the y-value decreases by 4 units. The function drops 4 times faster than x increases.
Yes! For linear functions, rate of change and slope are exactly the same thing. Both describe how steep the line is and in which direction.
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