Answer:
[tex]\large\boxed{y=\dfrac{5}{2}x+12}[/tex]
Step-by-step explanation:
n > 0
f(x + n) - shift the graph n units to the left
f(x - n) - shift the graph n units to the right
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
[tex]y=\dfrac{5}{2}x+2\to f(x)=\dfrac{5}{2}x+2[/tex]
translate the graph 4 units to the left:
[tex]f(x+4)=\dfrac{5}{2}(x+4)+2[/tex] use the distributive property
[tex]f(x+4)=\left(\dfrac{5}{2}\right)(x)+\left(\dfrac{5}{2}\right)(4)+2\\\\f(x+4)=\dfrac{5}{2}x+(5)(2)+2\\\\f(x+4)=\dfrac{5}{2}x+10+2\\\\f(x+4)=\dfrac{5}{2}x+12[/tex]
