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