Answer:
The equation of the line passing through the points (4, 2) and (2, 4) is y = -x + 6.
Explanation:
Given the points (4, 2) and (2, 4), we can use the point-slope form of a line, which is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.
To find the slope m, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values for the two points, we get:
m = (4 - 2) / (2 - 4) = 2 / -2 = -1
Next, we'll substitute one of the points and the slope into the point-slope form:
y - 2 = -1 (x - 4)
Expanding the right-hand side, we get:
y - 2 = -x + 4
Adding x and 2 to both sides, we get:
y = -x + 6
So, the equation of the line passing through the points (4, 2) and (2, 4) is y = -x + 6.