Question

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

Answer 1

Answer:

$\large\boxed{y=\dfrac{5}{2}x+12}$

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

$y=\dfrac{5}{2}x+2\to f(x)=\dfrac{5}{2}x+2$

translate the graph 4 units to the left:

$f(x+4)=\dfrac{5}{2}(x+4)+2$     use the distributive property

$f(x+4)=\left(\dfrac{5}{2}\right)(x)+\left(\dfrac{5}{2}\right)(4)+2\\\\f(x+4)=\dfrac{5}{2}x+(5)(2)+2\\\\f(x+4)=\dfrac{5}{2}x+10+2\\\\f(x+4)=\dfrac{5}{2}x+12$