The slope-point form of a line:
[tex]y-y_0=m(x-x_0)[/tex]
We have
[tex]m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1[/tex]
Substitute:
[tex]y-1=\dfrac{3}{4}(x-4)[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
Solve for y:
[tex]y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2[/tex]
Answer: D.
