Answer:
[tex]\large\boxed{y=\dfrac{7}{2}x-2}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the point (4, 12), and y-intercept b = -2 → (0, -2).
Substitute:
[tex]m=\dfrac{-2-12}{0-4}=\dfrac{-14}{-4}=\dfrac{14:2}{4:2}=\dfrac{7}{2}[/tex]
Finally:
[tex]y=\dfrac{7}{2}x-2[/tex]
