To derive the point-slope equation of a line, we can use the formula \(\( y - y_1 = m(x - x_1) \)\). Here, \(\( (x_1, y_1) \)\) represents a point on the line, and \(\( m \)\) stands for the slope of the line.
For this specific problem:
- The slope, \(\( m \)\), is 2.
- The point \(\((x_1, y_1)\)\) the line passes through is \(\((-5, -1)\)\).
Plugging these values into the point-slope formula, we get:
\(\[ y - (-1) = 2(x - (-5)) \]\)
Simplifying the equation, we obtain:
\(\[ y + 1 = 2(x + 5) \]\)
So, the point-slope equation of the line with the given slope and point is:
\(\[ y + 1 = 2(x + 5) \]\)
