First, determine the slope of the given line.
x + 2y = 6
Solve for y to get this in slope-intercept form. Remember to switch signs when you switch sides.
2y = -x + 6
Divide all terms on both sides by 2.
y = -0.5 x + 3
So the slope of the given line is the coefficient of x, which is -0.5 = -1/2
The slope of a perpendicular line is the negative reciprocal of that slope, which would be 2.
Use the point-slope form to build the equation with the point (4,2)
y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
y - 2 = 2(x - 4)
This is an equation that satisfies the question. To get this into slope-intercept form, expand, simplify and solve for y.
y = 2x - 8 + 2
y = 2x - 6