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:
5 is NOT a solution to the equation.
t = 6
Step-by-step explanation:
Step 1: Write out equation
2t - 1 = 11
Step 2: Add 1 to both sides
2t = 12
Step 3: Divide both sides by 2
t = 6
Answer:
The Greatest possible value of one of the integer is 140.
Step-by-step explanation:
Given: The average (arithmetic mean) of five different positive integers is 30.
To find: What is the greatest possible value of one of these integers?
Explanation: we are given that the arithmetic mean of five positive integer
is 30.
Let the five positive integers are A,B,C,D,E
The arithmetic mean :
=30.
On multiplying both side by 5.
A+B+C+D+E =150.
The least values of A ,B,C and D can be 1 ,2,3,4.
Then : 1 +2+3+4+E =150
On simplification 10+E =150
On subtraction both side by 10 we get
E = 140 .
Therefore, the Greatest possible value of one of the integer is 140.
Answer:
Have you ever had a dream that, that, um, that you had, uh, that you had to, you could, you do, you wit, you wa, you could do so, you do you could, you want, you wanted him to do you so much you could do anything?
Step-by-step explanation: