Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

DJ graphed the line [tex]\( y = -\frac{1}{2}x + 1 \)[/tex] on the coordinate plane below, but he made a mistake. Which of the following statements best describes DJ's mistake?

A. The [tex]\( y \)[/tex]-intercept is plotted as positive 1 when it should be plotted at negative 1.
B. The rate of change of the line is graphed as the reciprocal.
C. The rate of change of the line is positive when it should be graphed as a negative rate of change.
D. The [tex]\( y \)[/tex]-intercept is plotted at 1 when it should be plotted at [tex]\(-\frac{1}{2}\)[/tex].

Sagot :

GinnyAnswer
Let's carefully analyze the problem and the given choices to determine which statement best describes DJ's mistake.

First, we should identify the correct components of the equation [tex]\( y = -\frac{1}{2}x + 1 \)[/tex]:
- The y-intercept is 1. This means the line crosses the y-axis at the point (0, 1).
- The slope of the line is [tex]\(-\frac{1}{2}\)[/tex]. This indicates that for every unit the line moves to the right along the x-axis, it moves down by [tex]\(\frac{1}{2}\)[/tex] units along the y-axis, representing a negative rate of change.

Now let's examine the given statements one by one to identify DJ's mistake:

1. The y-intercept is plotted as a positive 1 when it should be plotted at negative 1.
- This statement is incorrect. The correct y-intercept from the equation [tex]\( y = -\frac{1}{2}x + 1 \)[/tex] is indeed positive 1, not negative 1.

2. The rate of change of the line is graphed as the reciprocal.
- This statement suggests that instead of using the slope [tex]\(-\frac{1}{2}\)[/tex], DJ used its reciprocal [tex]\(-2\)[/tex]. This is incorrect, as the equation gives the slope as [tex]\(-\frac{1}{2}\)[/tex].

3. The rate of change of the line is positive when it should be graphed as a negative rate of change.
- This statement suggests that DJ graphed the line with a positive slope instead of a negative one. Since the equation [tex]\( y = -\frac{1}{2}x + 1 \)[/tex] has a negative slope of [tex]\(-\frac{1}{2}\)[/tex], a mistake involving plotting a positive slope would imply DJ mistakenly made the line ascend as one moves to the right, contrary to the intended descent. This possibility accurately reflects a common mistake.

4. The y-intercept is plotted at 1 when it should be plotted at [tex]\(-\frac{1}{2}\)[/tex].
- This statement incorrectly suggests that the y-intercept should be [tex]\(-\frac{1}{2}\)[/tex] when it is actually 1.

Based on this analysis, the most appropriate statement indicating DJ's mistake would be:

The rate of change of the line is positive when it should be graphed as a negative rate of change.
Thus, the correct answer is:
3
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.