Question

Find the value of \(k\) so that the line through the given points has slope \(m .\) $$ (k+1, k-1),(k,-k) ; m=k+1 $$

Short answer

The value of \(k\) that makes the slope of the line equal to \(k+1\) is 0.

Step-by-step solution

Write Down Slope Formula

The basic formula calculating the slope of a line passing through two points \((x1, y1)\) and \((x2, y2)\) is given by \(m = (y2 - y1) / (x2 - x1)\).

Substitution

Substitute the coordinates of the given points into the slope formula, resulting in \(m = (k+1 - (-k)) / ((k+1) - k)\).

Simplify The Equation

After substituting, simplify the equation which gives \(m = 2k+1\).

Solve The Equation

We already know that \(m = k + 1\), so replace \(m\) in the equation obtained in step 3, giving us \(k + 1 = 2k + 1\).

Final Solution

Lastly, solve the equation for \(k\). Simplifying gives \(0 = k\).