Jaclyn used the slope formula to find the slope of the line through the points given in the table.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
0 & 4 \\
\hline
-3 & 0 \\
\hline
\end{tabular}

1. Point 1: [tex]$(0, 4)$[/tex]; Point 2: [tex]$(-3, 0)$[/tex]
2. Slope [tex]$=\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{-3 - 0} = \frac{-4}{-3}$[/tex]
3. Slope [tex]$=\frac{4}{3}$[/tex]

In which step did Jaclyn make an error?

A. In step 1, she switched the [tex]$x$[/tex] and [tex]$y$[/tex] values in point 2.
B. In step 2, she used the wrong formula or values.
C. In step 3, she simplified the slope incorrectly.
D. Jaclyn did not make an error.



Answer :

To determine in which step Jaclyn made an error, let's analyze her approach step-by-step:

1. Jaclyn's List of Points:

- Point 1: [tex]\((0, 4)\)[/tex]
- Point 2: [tex]\((-3, 0)\)[/tex]

2. Correct Setup for Slope Calculation:

To calculate the slope of the line through these points, we use the slope formula:

[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Plugging in the values from the points provided:

[tex]\[ y_1 = 4, \quad x_1 = 0, \quad y_2 = 0, \quad x_2 = -3 \][/tex]

3. Jaclyn's Calculation of the Slope:

Jaclyn's calculation is as follows:

[tex]\[ \text{slope} = \frac{0 - 4}{-3 - 0} = \frac{-4}{-3} \][/tex]

4. Simplification:

Simplifying the fraction:

[tex]\[ \frac{-4}{-3} = \frac{4}{3} = 1.3333333333333333 \][/tex]

Now, compare Jaclyn's calculation step-by-step:

- Step 1: Identified Points
- Jaclyn correctly identified the coordinates of the points.
- No error here.

- Step 2: Setting up the Slope Formula
- She used [tex]\(\frac{0 - 4}{-3 - 0}\)[/tex], which correctly corresponds to [tex]\(\frac{y_2 - y_1}{x_2 - x_1}\)[/tex].
- No error in the structure of the formula.
- However, here she made an error by switching [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates in the step. She used [tex]\( (0, -3) \)[/tex] and [tex]\( (4, 0) \)[/tex] instead of [tex]\( (0, 4) \)[/tex] and [tex]\( (-3, 0) \)[/tex].

- Step 3: Simplification
- Given that her setup already started incorrectly, her simplification yielded [tex]\(\frac{4}{3}\)[/tex], which would be correct for her mixed-up coordinates.

Thus, Jaclyn made an error in Step 1 where she switched the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values in point 2.

The correct answer is:
In step 1, she switched the [tex]$x$[/tex] and [tex]$y$[/tex] values in point 2.