Final answer:
To find the equation of the line perpendicular to 2y-4x=6 and passing through the point (4,6), we can determine the slope of the given line and then find the negative reciprocal of that slope. Using the point-slope form of a linear equation, we can write the equation of the line as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line. Substituting the values, we get y = -1/2x + 8.
Step-by-step explanation:
To find the equation of the line perpendicular to 2y-4x=6 and passing through the point (4,6), we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line in slope-intercept form is y = 2x + 3.
So, the slope of the given line is 2.
The negative reciprocal of 2 is -1/2.
Therefore, the slope of the line perpendicular to the given line is -1/2.
Using the point-slope form of a linear equation, we can write the equation of the line as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
Substituting the values, we get y - 6 = -1/2(x - 4).
Simplifying the equation, we get y = -1/2x + 8.