The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, 95) and (11, 12). Substitute:
[tex]m=\dfrac{12-95}{11-3}=-\dfrac{83}{8}[/tex]
[tex]\boxed{y-95=-\dfrac{83}{8}(x-3)}[/tex] point-slope form
Convert to the slope-ntercept form (y = mx + b)
[tex]y-95=-\dfrac{83}{8}(x-3)[/tex] use the distributivie property
[tex]y-95=-\dfrac{83}{8}x+\dfrac{249}{8}[/tex] add 95 to both sides
[tex]y=-\dfrac{83}{8}x+\dfrac{249}{8}+95\\\\y=-\dfrac{83}{8}x+\dfrac{249}{8}+\dfrac{760}{8}[/tex]
[tex]\boxed{y=-\dfrac{83}{8}x+\dfrac{1009}{8}}[/tex] slope-intercept form
Convert to the standrd form (Ax + By = C)
[tex]y=-\dfrac{83}{8}x+\dfrac{1009}{8}[/tex] multiply both sides by 8
[tex]8y=-83x+1009[/tex] add 83x to both sides
[tex]\boxed{83x+8y=1009}[/tex] standard form
