The answer is: "
y = −
x − 4 " .
_________________________________________________________Explanation:_________________________________________________________Given a linear equation in "slope-intercept form" ; that is:
"
y = mx + b " ;
________________________________________________A line that is PARALLEL to the aforementioned equation has the same slope (i.e the same value for "m" ) ; and the given the [x and y coordinates of any particular point] on the parallel line; " (x₁ , y₁)" ; we can write the equation of the parallel line—in "slope-intercept format" — by using the following equation/formula:
y − y₁ = m(x − x₁<span>) ;
</span>
in which: "m = the slope"
and plug in the values for: "m" ; and "x₁" and "y₁" ;
We are given the coordinates of a particular point on the line that is parallel:
" (-4, 1) " ;
as such: x₁ = -4 ; y₁ = 1 ;
& we are given: "m = −

" .
_____________________________________________So:
→ y − y₁ = m(x − x₁) ;
→ y − 1 = −

[x − (-4) ] ;
→ y − 1 = −

(x + 4) ;
→ y − 1 = −

(x + 4) ;
Now; let us examine the "right-hand side of the equation" ;
We have: −

(x + 4) ;
__________________________________________________Note the "distributive property" of multiplication:__________________________________________a(b + c) = ab + ac ;a(b – c) = ab – ac .__________________________________________As such:
__________________________________________ −

* x + (−

* 4) ;
= −

* x + (−

*

) ;
Note: Examine the
" (−

*

) " ;
→ EACH of the 2 (TWO) "4's" cancel out to "1"s" ;
{ since: "4 ÷ 4 = 1" } ;
and we can rewrite the: "(−

*

) " ;
as: " (−

*

) " ;
Note that: "{-5 ÷ 1 = -5} ; and: "{1 ÷ 1 = 1} ;
so, rewrite the: "" (−

*

) " ;
as: "{-5 * 1}" → which equals: = " -5" ;
So:
−

* x + (−

*

) ;
= -

x + (-5) ;
= -

x − 5 ;
______________________________________________→ Now, bring down the "y −1" ; which goes on the left hand side;
→ y − 1 = -

x − 5 ;
Add "1" to EACH SIDE of the equation; to isolate "y" as a single variable on the "left-hand side" of the equation ; & to write the equation of the particular parallel line in "slope-intercept format" ;
→ y − 1 + 1 = -

x − 5 + 1 ;
_______________________________________________________to get:
_______________________________________________________→ "
y = −
x − 4 " .
_______________________________________________________
Answer:
the correct answer is j=12+7
Options
The circle at the new location has _____________ the original circle.
- the same center as
- twice the circumference of
- half the radius of
- the same area as
Answer:
the same area as
Step-by-step explanation:
When a circle is translated and reflected, the center of the circle will change; however, its area, circumference, radius and diameter remain the same.
This is so because, translation and reflection only affect the positioning of the circle not the size.
Considering the above analysis, we can conclude that option d answers the question correctly.