Considering the graph of a line with a negative slope, which of the following could be true? Check all that apply.A.As the absolute value of the negative slope gets bigger, the graph of the line gets steeper.B.As the absolute value of the negative slope gets smaller, the graph of the line gets less steep.C.The line goes down from left to right.D.The line goes up from left to right.E.The line shifts down.
Question
Considering the graph of a line with a negative slope, which of the following could be true? Check all that apply.A.As the absolute value of the negative slope gets bigger, the graph of the line gets steeper.B.As the absolute value of the negative slope gets smaller, the graph of the line gets less steep.C.The line goes down from left to right.D.The line goes up from left to right.E.The line shifts down.
Solution
A. True - As the absolute value of the negative slope gets bigger, the graph of the line does get steeper. This is because the slope of a line is a measure of its steepness. A larger absolute value of the slope means a steeper line.
B. True - As the absolute value of the negative slope gets smaller, the graph of the line gets less steep. This is the opposite of the previous statement. A smaller absolute value of the slope means a less steep line.
C. True - A line with a negative slope does go down from left to right. This is the definition of a negative slope: as you move from left to right, the line goes down.
D. False - A line with a negative slope does not go up from left to right. This is the definition of a positive slope, not a negative one.
E. False - The slope of a line does not affect its vertical position, or "shift," on the graph. The vertical position of a line is determined by its y-intercept, not its slope.
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