Answer:
[tex]\large\boxed{y-\dfrac{1}{3}=\dfrac{3}{4}(x-4)\leftarrow\text{point-slope form}}\\\boxed{y=\dfrac{3}{4}x-2\dfrac{2}{3}\leftarrow\text{slope-intercept form}}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have
slope [tex]m=\dfrac{3}{4}[/tex]
point [tex]\left9,\ \dfrac{1}{3}\right)\to x_1=4,\ y_1=\dfrac{1}{3}[/tex]
Substitute:
[tex]y-\dfrac{1}{3}=\dfrac{3}{4}(x-4)[/tex]
Convert to the slope-intercept form (y = mx + b):
[tex]y-\dfrac{1}{3}=\dfrac{3}{4}x-3[/tex] add 1/3 to both sides
[tex]y=\dfrac{3}{4}x-2\dfrac{2}{3}[/tex]
