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.
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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:
\[ m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3 \]
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Identify the y-intercept (b): Since one of the points is (0, -4), we can see that the y-intercept \( b \) is -4.
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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).