The slope-intercept form:
[tex]y=mx+b[/tex]
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-4, 47) and (2, -16). Substitute:
[tex]m=\dfrac{-16-47}{2-(-4)}=\dfrac{-63}{6}=-\dfrac{63:3}{6:3}=-\dfrac{21}{2}[/tex]
Therefore we have:
[tex]y=-\dfrac{21}{2}x+b[/tex]
Put the coordinates of the point (2, -16) to the equation:
[tex]-16=-\dfrac{21}{2}(2)+b\\\\-16=-21+b\qquad\text{add 21 from both sides}\\\\5=b\to b=5[/tex]
Answer: [tex]\boxed{y=-\dfrac{21}{2}x+5}[/tex]
