Question

Find the value of r so that the line through (1,2) and (-5,r) has a slope of 1/2

Answer 1

The value of r is -1

Explanation:

The slope of a Line

Suppose a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

The points are (1,2) and (-5,r), and the slope is 1/2, thus

`\displaystyle (r-2)/(-5-1)=(1)/(2)`

Operating:

`\displaystyle (r-2)/(-6)=(1)/(2)`

Multiplying by -6:

`2(r-2)=-6`

Dividing by 2:

`r-2=-3`

Add 2:

`r=-3+2=-1`

`\boxed{r=-1}`

The value of r is -1