Question

question 3 of 10 considering the graph of a line with a negative slope, which of the following could be true? check all that apply. a. the line goes down from left to right. b. as the absolute value of the negative slope gets smaller, the graph of the line gets steeper. c. the line goes up from left to right. d. as the absolute value of the negative slope gets bigger, the graph of the line gets steeper. e. the line shifts down.

Explanation:

Step1: Understand slope concept

The slope $m$ of a line is given by $m=\frac{\Delta y}{\Delta x}$. A negative slope means $\frac{\Delta y}{\Delta x}<0$. When moving from left - to - right ($\Delta x>0$), $\Delta y < 0$, so the line goes down. Thus, A is correct and C is incorrect.

Step2: Analyze steepness and slope magnitude

The magnitude of the slope determines the steepness of the line. For a negative slope, as $|m|$ increases (the absolute value of the negative slope gets bigger), the line becomes steeper. When $|m|$ decreases (the absolute value of the negative slope gets smaller), the line becomes less steep. So D is correct and B is incorrect.

Step3: Consider vertical shift

The slope of a line does not determine vertical shift. The equation of a line is $y = mx + b$, where $b$ is the y - intercept and determines vertical shift. The slope $m$ does not cause a vertical shift. So E is incorrect.

Answer:

A. The line goes down from left to right., D. As the absolute value of the negative slope gets bigger, the graph of the line gets steeper.