Final answer:
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line first. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. The equation of the line that passes through the point (4,1) and is perpendicular to the line 2x - y = 4 is y = -1/2x + 3.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line first.
The given line has the equation 2x - y = 4. To find its slope, we need to rearrange the equation in the form y = mx + b, where m is the slope.
By rearranging the equation, we get y = 2x - 4. The slope of this line is 2.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is -1/2.
Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values (4, 1) for (x1, y1) and -1/2 form, we get the equation of the perpendicular line as y - 1 = -1/2(x - 4).
Simplifying the equation, we have y - 1 = -1/2x + 2.
Therefore, the equation of the line that passes through the point (4,1) and is perpendicular to the line 2x - y = 4 is y = -1/2x + 3.