The document provides the solution steps to determine the value of m given that the points (m,3) and (1,m) lie on a line with slope m, where m>0. It states that using the slope formula with the given point values results in an equation with (m-1) in the denominator. Multiplying both sides by (m-1) removes it from the denominator, leaving an equation that can be rearranged and solved for m, with the positive square root of 3 being the only value of m that satisfies the original constraints.

1. Problem of the Week Solution 2/22/10 Jen Markham

2. Original Problem Determine m given that m>0 and the points (m,3) and (1,m) lie on a line with slope m.

3. To find the value of m, plug the values of the points given into the slope formula.

4. Then multiply both sides of the equation by (m – 1) to get rid of the (m – 1) in the denominator on the left side of the equation.

5. After multiplying you are left with… You can then add m to both sides of the equation and get…

6. Then solve by taking the square root of both sides.

7. But… Since the original problem stated that m must be greater than zero, this means that m can only equal