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: Recall slope - direction relationship

The slope \(m=\frac{\Delta y}{\Delta x}\). For a negative slope, when \(x\) increases (\(\Delta x> 0\)), \(y\) decreases (\(\Delta y < 0\)). So the line goes down from left - to - right, making option A true and option C false.

Step2: Understand slope - steepness relationship

The steepness of a line is related to the absolute value of the slope. If \(m\) is negative, as \(|m|\) increases (e.g., from \(- 1\) to \(-3\)), the line becomes steeper. When \(|m|\) decreases (e.g., from \(-3\) to \(-1\)), the line becomes less steep. So option D is true and option B is false.

Step3: Analyze vertical shift

The slope of a line does not determine a vertical shift. A vertical shift is determined by a change in the \(y\) - intercept. So option E is not related to the slope value and is false.

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.