The slope-intercept form of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, -2) and (-2, 7). Substitute:
[tex]m=\dfrac{7-(-2)}{-2-(-1)}=\dfrac{9}{-1}=-9[/tex]
Therefore we have [tex]y=-9x+b[/tex].
Put the coordinates of the point (-1, -2) to the equation of a line:
[tex]-2=(-9)(-1)+b[/tex]
[tex]-2=9+b[/tex] subtract 9 from both sides
[tex]-11=b\to b=-11[/tex]
Answer: y = -9x - 11
