The given function is \( y = -2x + 8 \), which has a slope of -2. The slope indicates how steep the line is and the direction in which it moves. A negative slope means that as \( x \) increases, \( y \) decreases.
If the slope is changed to -10, the new function would be \( y = -10x + 8 \).
Effects of Changing the Slope:
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Steepness of the Line: The new line will be steeper than the original line. A slope of -10 means that for every unit increase in \( x \), \( y \) decreases by 10 units, compared to the original slope of -2, where \( y \) decreases by only 2 units for the same increase in \( x \).
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Direction: Both lines will still slope downwards from left to right since both slopes are negative.
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Y-Intercept: The y-intercept remains the same at \( y = 8 \). This means both lines will intersect the y-axis at the point (0, 8).
In summary, changing the slope from -2 to -10 makes the graph of the function steeper, while keeping the same y-intercept. This means that the new line will fall more sharply as you move from left to right.