78. Find the slope of the line and the segment it intercepts on the y-axis, given that the line passes through the points $M(2, -1)$ and $P(-1, 8)$.
Solution. We will use the equation of a straight line passing through two given points (5). Substituting into the equation instead of $x_{1}, y_{1}, x_{2}, y_{2}$ the coordinates of points $M$ and $P$, we get

$$
\frac{y-(-1)}{8-(-1)}=\frac{x-2}{-1-2}
$$

hence

$$
\frac{y+1}{9}=\frac{x-2}{-3} \text { or } y+1=-3(x-2)
$$

i.e.

$$
y=-3 x+5
$$

The desired equation of the straight line has been reduced to the slope-intercept form, i.e., to the form $y=k x+b$.

Thus, the slope of the desired straight line $k=-3$ and the y-intercept $b=5$.

The slope can also be found using formula (6):

$$
k=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-(-1)}{-1-2}=-3
$$