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

3 answers

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).

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

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).