Answer:
[tex]y = \frac{1}{2}x - 4[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{1}{2}x[/tex]
Required
Shift [tex]3\ units[/tex] down and [tex]2\ units[/tex] right
[tex]y = \frac{1}{2}x[/tex]
Shift 3 units down
The rule is: (x,y)=> (x,y-a)
Where a is the number of units shifted down
In this case: [tex]a = 3[/tex]
So, we have:
[tex]y = \frac{1}{2}x[/tex] == > [tex]y = \frac{1}{2}x - 3[/tex]
Shift 2 units right
The rule is: (x,y)=>(x-b,y)
Where b is the number of units shifted right
In this case: [tex]b = 2[/tex]
So, we have:
[tex]y = \frac{1}{2}x - 3[/tex] ==> [tex]y = \frac{1}{2}(x - 2) - 3[/tex]
Open bracket:
[tex]y = \frac{1}{2}x - 1 - 3[/tex]
[tex]y = \frac{1}{2}x - 4[/tex]
Hence, the new equation after the transformation is:
[tex]y = \frac{1}{2}x - 4[/tex]
