Find the value of k so that the line through the given points has slope m.
(2k, 3), (1, k); m = 2
slope = (y2 - y1)/(x2 - x1)
so, [(k-3)/(1-2k)] = 2
(k-3) = 2(1-2k)
=> k = 1
To find the value of k such that the line passing through the points (2k, 3) and (1, k) has a slope of m = 2, we can use the formula for calculating the slope of a line:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two given points.
Let's substitute the given points into the formula:
m = (k - 3) / (1 - 2k)
Now, we need to solve this equation for k.
Multiply both sides of the equation by (1 - 2k) to eliminate the denominator:
m(1 - 2k) = k - 3
Expand the left side:
m - 2mk = k - 3
Rearrange the equation:
k - 2mk = m - 3
Factor out k:
k(1 - 2m) = m - 3
Divide both sides of the equation by (1 - 2m):
k = (m - 3) / (1 - 2m)
Now, substitute the given slope m = 2 into the equation:
k = (2 - 3) / (1 - 2(2))
Simplify the expression:
k = (-1) / (1 - 4)
k = (-1) / (-3)
k = 1/3
Therefore, the value of k that satisfies the given conditions is 1/3.