Question

The points (5, r) and (10, -1) lie on a line with slope 5. Find the missing coordinate r

Answer 1

Answer: r=-26

Explanation:

`\displaystyle\\(5,r)\ \ \ \ (10,1)\ \ \ \ slope \ m=5\\\\\boxed {m=(y_2-y_1)/(x_2-x_1) }\\\\x_1=5\ \ \ \ \ x_2=10\ \ \ \ \ y_1=r\ \ \ \ y_2=-1\ \ \ \ \ m=5\\\\Hence,\\\\5=(-1-r)/(10-5) \\\\5=(-1-r)/(5)`

Multiply both parts of the equation by 5:

`5(5)=-1-r\\\\25=-1-r\\\\25+r=-1-r+r\\\\25+r=-1\\\\25+r-25=-1-25\\\\r=-26`