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?
To determine the rate of change of the linear function , we need to identify the structure of the equation. We notice that it is given in the slope-intercept form , where is the slope or the rate of change.
In the equation , the term involving is . Thus, the coefficient of , which is , represents the rate of change or slope of the function.
Therefore, the rate of change of the function is .
For the function in front of you, the slope is?
The rate of change is how much y increases for each unit increase in x. In , the coefficient of x is 5, meaning y increases by 5 for every 1-unit increase in x.
The 14 is the y-intercept - it's where the line crosses the y-axis when x = 0. It's not related to the rate of change at all!
No! Both forms are equivalent. The order of terms doesn't change their meaning. The coefficient of x is still 5 in both cases.
Think: "The slope is stuck to x!" Whatever number is multiplied by x (the coefficient) is always the slope or rate of change.
If you see just x (like in y = x + 3), there's an invisible 1 in front of it. So the slope would be 1, meaning the rate of change is 1.
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