The problem is: Find an equation for the line, in general form, with the given properties: slope =4; containing the point (-2, -4)
point slope ... y + 4 = 4 (x + 2)
slope-intercept ... y = 4 x + 4
manipulate into general form
To find the equation of a line in general form when given the slope and a point, you can use the point-slope form of a linear equation and then convert it to the general form.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents a point on the line, and m represents the slope of the line.
In this case, the given slope is 4, and the line contains the point (-2, -4). Applying the point-slope form, we have:
y - (-4) = 4(x - (-2))
Simplifying, we get:
y + 4 = 4(x + 2)
Expanding the brackets:
y + 4 = 4x + 8
To put the equation in general form, we want to express it as Ax + By + C = 0, where A, B, and C are integers without common factors.
Moving all the terms to the left side of the equation:
4x - y + 4 - 8 = 0
Simplifying further:
4x - y - 4 = 0
So, the equation of the line in general form with the given properties is 4x - y - 4 = 0.