Question
. Ms. Hawkins gave her students a table of values representing a linear function.
x y
‒2 ‒8.5
4 ‒7
12 ‒5
Which students correctly wrote an equation to represent the function?
A. Alice only
B. Alice and Joseph
C. Susan and Joseph
D. All three students are correct.
Susan
y + 7 = 4(x – 4)
Joseph
x – 4y = 32
Alice
= − 1 8
4
x y
‒2 ‒8.5
4 ‒7
12 ‒5
Which students correctly wrote an equation to represent the function?
A. Alice only
B. Alice and Joseph
C. Susan and Joseph
D. All three students are correct.
Susan
y + 7 = 4(x – 4)
Joseph
x – 4y = 32
Alice
= − 1 8
4
Answers
GPT-4o mini
To determine which students correctly wrote an equation to represent the linear function based on the provided table of values, we can start by identifying the slope and y-intercept from the data points given.
The points from the table are:
1. (-2, -8.5)
2. (4, -7)
3. (12, -5)
### Step 1: Calculate the Slope (m)
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use two points for finding the slope. Let's use the points (4, -7) and (12, -5):
\[
m = \frac{-5 - (-7)}{12 - 4} = \frac{-5 + 7}{12 - 4} = \frac{2}{8} = \frac{1}{4}
\]
### Step 2: Find the Equation
We can use point-slope form \( y - y_1 = m(x - x_1) \) to find the equation. Let's use the point (4, -7):
\[
y - (-7) = \frac{1}{4}(x - 4)
\]
This simplifies to:
\[
y + 7 = \frac{1}{4}(x - 4)
\]
This is equivalent to:
\[
y + 7 = \frac{1}{4}x - 1
\]
Bringing it to slope-intercept form, \( y = mx + b \):
\[
y = \frac{1}{4}x - 8
\]
### Step 3: Check Each Student's Equation
**Susan:**
\[
y + 7 = 4(x - 4)
\]
This does not match our derived equation; it seems incorrect.
**Joseph:**
\[
x - 4y = 32
\]
Rearranging gives us:
\[
4y = x - 32 \implies y = \frac{1}{4}x + 8
\]
This does not match the derived equation, so he is incorrect.
**Alice:**
Alice’s equation appears incomplete, but if it implies the slope of \( -\frac{1}{8} \), it also does not match our derived slope of \( \frac{1}{4} \).
### Conclusion
None of the students wrote the correct equation based on the analysis of the data. Therefore, the correct answer is:
**None of the given answer choices (A, B, C, D) is correct based on the equations provided by the students.**
If you are required to give an answer based on the options presented, it would be implied that none of them are correct. However, if this were a test scenario or practice problem, ensure to review the students' equations and match against the derived equation thoroughly.
The points from the table are:
1. (-2, -8.5)
2. (4, -7)
3. (12, -5)
### Step 1: Calculate the Slope (m)
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use two points for finding the slope. Let's use the points (4, -7) and (12, -5):
\[
m = \frac{-5 - (-7)}{12 - 4} = \frac{-5 + 7}{12 - 4} = \frac{2}{8} = \frac{1}{4}
\]
### Step 2: Find the Equation
We can use point-slope form \( y - y_1 = m(x - x_1) \) to find the equation. Let's use the point (4, -7):
\[
y - (-7) = \frac{1}{4}(x - 4)
\]
This simplifies to:
\[
y + 7 = \frac{1}{4}(x - 4)
\]
This is equivalent to:
\[
y + 7 = \frac{1}{4}x - 1
\]
Bringing it to slope-intercept form, \( y = mx + b \):
\[
y = \frac{1}{4}x - 8
\]
### Step 3: Check Each Student's Equation
**Susan:**
\[
y + 7 = 4(x - 4)
\]
This does not match our derived equation; it seems incorrect.
**Joseph:**
\[
x - 4y = 32
\]
Rearranging gives us:
\[
4y = x - 32 \implies y = \frac{1}{4}x + 8
\]
This does not match the derived equation, so he is incorrect.
**Alice:**
Alice’s equation appears incomplete, but if it implies the slope of \( -\frac{1}{8} \), it also does not match our derived slope of \( \frac{1}{4} \).
### Conclusion
None of the students wrote the correct equation based on the analysis of the data. Therefore, the correct answer is:
**None of the given answer choices (A, B, C, D) is correct based on the equations provided by the students.**
If you are required to give an answer based on the options presented, it would be implied that none of them are correct. However, if this were a test scenario or practice problem, ensure to review the students' equations and match against the derived equation thoroughly.