Final answer:
The equation of a line perpendicular to 2x - 4y = 6 and passing through the point (4,6) is y = -2x + 14, found by using the negative reciprocal of the original line's slope and the point-slope formula.
Step-by-step explanation:
To write the equation of a line that is perpendicular to another, we first need to understand the original line's slope. There appears to be a typo in the given equation '2x-4x=6'. Assuming the correct equation should be '2x - 4y = 6', we can rewrite it in slope-intercept form (y = mx + b) to find its slope. First, rearrange the equation to solve for y:
2x - 4y = 6
-4y = -2x + 6
y = (1/2)x - 3/2
The slope of this line is 1/2. A line that is perpendicular to this would have a slope that is the negative reciprocal, so our new line's slope is -2. With the point (4,6) and a slope of -2, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Replacing x1 with 4 and y1 with 6, and m with -2, we get:
y - 6 = -2(x - 4)
We can simplify this to get the equation in slope-intercept form:
y - 6 = -2x + 8
y = -2x + 14
This is the equation of the line that passes through the point (4,6) and is perpendicular to the line 2x - 4y = 6.