Question

The points (−5, -5) and (r, 1) lie on a line with slope 1/2. Find the missing coordinate r.

Answer 1

The slope is expressed as

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ where \\ (x_1,y_1)\text{ and} \\ (x_2,y_2)\text{ are the coordinates of points through which the line passes} \end{gathered}`

Given that the points (-5, -5) and (r, 1) lie on the line with slope 1/2, this implies that

`\begin{gathered} x_1=-5 \\ y_1=-5 \\ x_2=r \\ y_2=1 \end{gathered}`

By substituting these valus into the slope formula, we have

`\begin{gathered} (1)/(2)=(1-(-5))/(r-(-5)) \\ \Rightarrow(1)/(2)=(1+5)/(r+5) \\ cross-multiply, \\ r+5=2(1+5) \\ \Rightarrow r+5=12 \\ add\text{ -5 to both sides of the equation,} \\ r+5-5=12-5 \\ \Rightarrow r=7 \end{gathered}`

Hence, the missing coordinate r is evaluated to be

`7`