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.
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.
