To find the equation of the line that passes through the points (0, 2) and (5, -1), we can start by calculating the slope (m) of the line. The slope is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can take (x1, y1) = (0, 2) and (x2, y2) = (5, -1).
Calculating the slope:
\[ m = \frac{-1 - 2}{5 - 0} = \frac{-3}{5} \]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Substituting in one of the points and the slope we calculated:
\[ y - 2 = -\frac{3}{5}(x - 0) \]
This simplifies to:
\[ y - 2 = -\frac{3}{5}x \] \[ y = -\frac{3}{5}x + 2 \]
Now we can check which of the given responses matches this equation.
We recognize that we need to rewrite the equation in a form that matches one of the available choices. The choices listed do not include \(y = -\frac{3}{5}x + 2\), indicating that the correct equation may not have been provided in the responses.
It's possible to approximate the line equation based on the calculated slope \(-\frac{3}{5}\), but that doesn't clearly match any response given.
If we consider the original points, \(y=2\) is already the y-intercept when \(x=0\). At \(x=5\), we computed y as -1, which confirms our calculations are correct.
None of the supplied options appear to fit, indicating there may be an error in provided choices. Please double-check the corresponding responses to ensure they correspond to the determined slope and y-intercept.
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