For the following straight line equation, state what is the rate of change?
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For the following straight line equation, state what is the rate of change?
To solve this problem, we need to determine the rate of change of the linear equation given by:
The standard form for a linear equation is:
where represents the slope of the line. The slope indicates the rate of change of the function, which describes how much the value of changes for a unit change in .
In the equation , the slope is . This means that for every unit increase in , the value of decreases by 4. Thus, the rate of change for this equation is .
Therefore, the rate of change is .
Look at the graph below and determine whether the function's rate of change is constant or not:
A negative rate of change means the line is decreasing. As x increases by 1, y decreases by 4. This creates a downward-sloping line from left to right.
They're the same thing! Both terms describe how much y changes when x increases by 1. In , the slope and rate of change are both -4.
In form, the slope is always the coefficient of x (the number multiplying x). The other number is the y-intercept.
The number 3 is the y-intercept, not the rate of change. It tells us where the line crosses the y-axis when .
Yes! Pick any x-value, calculate y, then pick x + 1 and see if y decreases by 4. For example: when x = 1, y = -1; when x = 2, y = -5. The difference is -4 ✓
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