Answer:
The equation of the line is y = 1/2x + 5
Explanation:
To find a line perpendicular to the first line, we first need to find the slope of the first line. We can do this by solving for y.
6x + 3y = 2
3y = -6x + 2
y = -2x + 2/3
So, we know the original slope to be -2. Perpendicular lines have opposite and reciprocal slopes. Therefore, we know the new slope to be 1/2. Knowing this, we can use the slope and the point in point-slope form to find the equation.
y - y1 = m(x - x1)
y - 4 = 1/2(x + 2)
y - 4 = 1/2x + 1
y = 1/2x + 5