Question

Translate the graph of the equation y=5/2 x+2 to the left 4 units. Graph the translation

Answer 1

`\large\boxed{y=(5)/(2)x+12}`

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

`y=(5)/(2)x+2\to f(x)=(5)/(2)x+2`

translate the graph 4 units to the left:

`f(x+4)=(5)/(2)(x+4)+2` use the distributive property

`f(x+4)=\left((5)/(2)\right)(x)+\left((5)/(2)\right)(4)+2\\\\f(x+4)=(5)/(2)x+(5)(2)+2\\\\f(x+4)=(5)/(2)x+10+2\\\\f(x+4)=(5)/(2)x+12`