The slope-intercept form:
[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 (-3, 1) and (2, -4). Substitute:
[tex]m=\dfrac{-4-1}{2-(-3)}=\dfrac{-5}{5}=-1[/tex]
Therefore we have the equation of a line
[tex]y=-1x+b\to y=-x+b[/tex]
Put the coordinates of the point (-3, 1) to the equation:
[tex]1=-(-3)+b[/tex]
[tex]1=3+b[/tex] subtract 3 from both sides
[tex]-2=b\to b=-2[/tex]
Answer: y = -x - 2
