Question
Using the graph, derive the equation of the line in slope-intercept form.
(1,-1) (0,-4)
(1 point)
Responses
y=3x+4
y equals 3 x plus 4
y=−3x−4
y equals negative 3 x minus 4
y=3x−4
y equals 3 x minus 4
3x−y=4
3 x minus y equals 4
(1,-1) (0,-4)
(1 point)
Responses
y=3x+4
y equals 3 x plus 4
y=−3x−4
y equals negative 3 x minus 4
y=3x−4
y equals 3 x minus 4
3x−y=4
3 x minus y equals 4
Answers
Answered by
GPT-4o mini
To find the equation of the line passing through the points (1, -1) and (0, -4), we can use the slope-intercept form of the equation of a line, which is:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
1. **Calculate the slope (m):**
The slope \( m \) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (1, -1) and (0, -4):
- \((x_1, y_1) = (1, -1)\)
- \((x_2, y_2) = (0, -4)\)
Substituting into the slope formula:
\[
m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3
\]
2. **Identify the y-intercept (b):**
Since one of the points is (0, -4), we can see that the y-intercept \( b \) is -4.
3. **Write the equation:**
Now that we have the slope \( m = 3 \) and the y-intercept \( b = -4 \), we can write the equation of the line:
\[
y = 3x - 4
\]
Therefore, the correct response is:
**y = 3x - 4** (y equals 3 x minus 4).
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
1. **Calculate the slope (m):**
The slope \( m \) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (1, -1) and (0, -4):
- \((x_1, y_1) = (1, -1)\)
- \((x_2, y_2) = (0, -4)\)
Substituting into the slope formula:
\[
m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3
\]
2. **Identify the y-intercept (b):**
Since one of the points is (0, -4), we can see that the y-intercept \( b \) is -4.
3. **Write the equation:**
Now that we have the slope \( m = 3 \) and the y-intercept \( b = -4 \), we can write the equation of the line:
\[
y = 3x - 4
\]
Therefore, the correct response is:
**y = 3x - 4** (y equals 3 x minus 4).
Answer
Write the equation of the line in slope-intercept form.
(0,1)
(1,-4)
(1 point)
Responses
−5x−y=−1
negative 5 x minus y equals negative 1
y=5x+1
y equals 5 x plus 1
y=−5x−1
y equals negative 5 x minus 1
y=−5x+1
(0,1)
(1,-4)
(1 point)
Responses
−5x−y=−1
negative 5 x minus y equals negative 1
y=5x+1
y equals 5 x plus 1
y=−5x−1
y equals negative 5 x minus 1
y=−5x+1
Answered by
GPT-4o mini
To find the equation of the line that passes through the points (0, 1) and (1, -4), we can follow these steps:
1. **Calculate the slope (m):**
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 1) and (1, -4):
- \((x_1, y_1) = (0, 1)\)
- \((x_2, y_2) = (1, -4)\)
Substituting into the slope formula:
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]
2. **Identify the y-intercept (b):**
Since one of the points is (0, 1), the y-intercept \( b \) is clearly 1.
3. **Write the equation:**
Now that we have the slope \( m = -5 \) and the y-intercept \( b = 1 \), we can write the equation of the line:
\[
y = -5x + 1
\]
Therefore, the correct response is:
**y = -5x + 1** (y equals negative 5 x plus 1).
1. **Calculate the slope (m):**
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 1) and (1, -4):
- \((x_1, y_1) = (0, 1)\)
- \((x_2, y_2) = (1, -4)\)
Substituting into the slope formula:
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]
2. **Identify the y-intercept (b):**
Since one of the points is (0, 1), the y-intercept \( b \) is clearly 1.
3. **Write the equation:**
Now that we have the slope \( m = -5 \) and the y-intercept \( b = 1 \), we can write the equation of the line:
\[
y = -5x + 1
\]
Therefore, the correct response is:
**y = -5x + 1** (y equals negative 5 x plus 1).