To find the equation of the line passing through the points \((-1, 5)\) and \((1, -2)\), we first need to determine the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where \((x_1, y_1) = (-1, 5)\) and \((x_2, y_2) = (1, -2)\):
\[ m = \frac{-2 - 5}{1 - (-1)} = \frac{-7}{2} \div 2 = -\frac{7}{2} \]
Now that we have the slope, we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
Using point \((-1, 5)\):
\[ y - 5 = -\frac{7}{2}(x - (-1)) \]
Simplifying:
\[ y - 5 = -\frac{7}{2}(x + 1) \] \[ y - 5 = -\frac{7}{2}x - \frac{7}{2} \] \[ y = -\frac{7}{2}x - \frac{7}{2} + 5 \] \[ y = -\frac{7}{2}x + \frac{3}{2} \]
Therefore, the equation of the line is:
\[ y = -\frac{7}{2}x + \frac{3}{2} \]
So the correct option is:
y equals negative Start Fraction 7 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction