Question

The points (-3, -3) and (5, r) lie on a line with slope 3/2 Find the missing coordinate r.

Answer 1

Answer:

The missing coordinate $r$ is 9.

Step-by-step explanation:

Given the points $P(x,y) = (-3,-3)$ and $Q(x,y) = (5,r)$, the slope of a line passing the two points ($m_{PQ}$) is determined by equation of secant line:

$m_{PQ} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}$ (1)

$m_{PQ} = \frac{r-(-3)}{5-(-3)}$

If we know that $m_{PQ} = \frac{3}{2}$, then the value of $r$ is:

$\frac{3}{2} = \frac{r+3}{8}$

$12 = r + 3$

$r = 9$

The missing coordinate $r$ is 9.