To find the equation of a line that passes through the point \((-4, 5)\) with a slope of \(-2\), we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
Here, \(m\) is the slope, and \((x_1, y_1)\) is the point through which the line passes. Substituting in the values:
- \(m = -2\)
- \(x_1 = -4\)
- \(y_1 = 5\)
We can plug in these values:
\[ y - 5 = -2(x - (-4)) \]
This simplifies to:
\[ y - 5 = -2(x + 4) \]
Now, distribute the \(-2\):
\[ y - 5 = -2x - 8 \]
Next, we add \(5\) to both sides to solve for \(y\):
\[ y = -2x - 8 + 5 \] \[ y = -2x - 3 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -2x - 3 \]