Given :
We are given the slope m = -2 and a point on the line (-2, -3).
To find :
The equation for the line in slope-intercept form
Solution :
We can use the point-slope form of the equation of a line to find the slope-intercept equation of the line:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point on the line.
Substituting the given values, we get:
y - (-3) = -2(x - (-2))
Simplifying:
y + 3 = -2(x + 2)
Expanding:
y + 3 = -2x - 4
Subtracting three from both sides:
y = -2x - 7
Therefore, the equation of the line that passes through the point (-2, -3) and has a slope of -2 is :
y = -2x - 7.