Answer :
Answer:
[tex]\large\boxed{y=-\dfrac{3}{2}x+16\dfrac{1}{2}\to y=-1.5x+16.5}[/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
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, 12) and (5, 9).
Substitute:
[tex]m=\dfrac{9-12}{5-3}=\dfrac{-3}{2}=-\dfrac{3}{2}[/tex]
Put the value of a slope and coordinates of the point (3, 12) to the equation of a line:
[tex]12=-\dfrac{3}{2}(3)+b[/tex]
[tex]12=-\dfrac{9}{2}+b[/tex]
[tex]12=-4\dfrac{1}{2}+b[/tex] add [tex]4\dfrac{1}{2}[/tex] to both sides
[tex]16\dfrac{1}{2}=b\to b=16\dfrac{1}{2}[/tex]
Finally:
[tex]y=-\dfrac{3}{2}x+16\dfrac{1}{2}[/tex]