Final answer:
The equation of the line passing through the point (-2,-3) with a slope of 2 is y = 2x + 1.
Step-by-step explanation:
To find the equation of a line that passes through the point (-2,-3) with a slope of 2, we use the point-slope form of a linear equation: y - y1 = m(x - x1). The point (-2,-3) gives us the values for x1 and y1, while the slope (m) is given as 2. Substituting these values into the point-slope form equation yields:
y - (-3) = 2(x - (-2))
This simplifies to:
y + 3 = 2(x + 2)
Expanding the equation we get:
y + 3 = 2x + 4
Finally, subtracting 3 from both sides to get y by itself, the equation of the line is:
y = 2x + 1