Consider the function y=8-2x. What is the effect on the graph for the given function if the slope of the function is changed to -10
If the slope of the function is changed to -10, the equation of the new function would be y = -10x + b, where b is a constant term.
The original function y=8-2x has a slope of -2. The change in slope from -2 to -10 means the new graph would be steeper, as the absolute value of the slope increased. The negative sign indicates that the line will be sloping downwards from left to right.
The value of b does not affect the slope but it shifts the graph vertically.
To understand the effect on the graph if the slope of the function y = 8 - 2x is changed to -10, we can compare the two functions.
The original function, y = 8 - 2x, has a slope of -2. This means that for every increase of 1 in the x-value, the y-value decreases by 2.
If we change the slope to -10, the new function becomes y = 8 - 10x. This means that for every increase of 1 in the x-value, the y-value decreases by 10.
Here, we can see that the new function has a steeper slope compared to the original one. This means that the graph will become steeper as well.
To visualize this, let's compare the graphs of both functions.
Graph of the original function y = 8 - 2x:
| *
8 | *
| *
| *
2 | *
| *
| *
-4 | *
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-4 -2 0 2 4
Graph of the new function y = 8 - 10x:
| *
8 |
|
|
2 | *
|
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-14 | *
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-4 -2 0 2 4
As you can see from the graphs, the new function y = 8 - 10x has a steeper slope compared to the original function y = 8 - 2x. The points on the new graph are further apart, indicating a greater change in the y-values for a given change in the x-values.
To determine the effect of changing the slope of the function y=8-2x to -10, we need to understand the relationship between slope and the graph of a linear equation.
The slope of a linear function determines the steepness or incline of the graph. A positive slope indicates an upward incline, while a negative slope indicates a downward incline. A slope of zero represents a horizontal line.
In the given function y=8-2x, the slope is -2. This means that for every unit increase in x, y decreases by 2 units. The graph of this function is a line with a negative slope.
Now, if we change the slope to -10, the new function becomes y=8-10x. This new slope is even steeper than the previous slope of -2. It means that for every unit increase in x, y will decrease by 10 units.
The effect on the graph is that the line will become much steeper, with a steeper downward incline. The points on the graph will be more closely packed together, indicating a faster rate of decrease in y as x increases.
In summary, changing the slope from -2 to -10 in the function y=8-2x will make the graph steeper, resulting in a faster decrease in the y-values as x increases.