Question

NEED HELP ASAP PLS!!!!!!!!

Answer 1

The answer is:  " y = −$\frac{5}{4}$  x − 4 " .
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Explanation:
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Given a linear equation in "slope-intercept form" ; that is:

" y = mx + b " ;
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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)  ;

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 = − $\frac{5}{4}$" .
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So:

               →  y − y₁ = m(x − x₁) ;

               →  y − 1    = − $\frac{5}{4}$ [x − (-4) ] ;

               →  y − 1    = − $\frac{5}{4}$ (x + 4) ;

               →  y − 1    = − $\frac{5}{4}$ (x + 4) ; 

      Now; let us examine the "right-hand side of the equation" ;

We have:     − $\frac{5}{4}$ (x + 4)      ; 
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Note the "distributive property" of multiplication:__________________________________________a(b + c) = ab + ac ;
a(b – c) = ab – ac .__________________________________________
As such:
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 − $\frac{5}{4}$ * x   +  (− $\frac{5}{4}$ * 4)  ;

   =  − $\frac{5}{4}$ * x  + (− $\frac{5}{4}$ * $\frac{4}{1}$)  ;

 Note:  Examine the " (− $\frac{5}{4}$ * $\frac{4}{1}$) " ; 

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

and we can rewrite the:  "(− $\frac{5}{4}$ * $\frac{4}{1}$) " ; 

as:  " (− $\frac{5}{1}$ * $\frac{1}{1}$) " ;

Note that:  "{-5 ÷ 1 = -5} ;  and: "{1 ÷ 1 = 1} ;

so, rewrite the:  "" (− $\frac{5}{1}$ * $\frac{1}{1}$) " ;

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


So: 

− $\frac{5}{4}$ * x  + (− $\frac{5}{4}$ * $\frac{4}{1}$)  ; 

=  - $\frac{5}{4}$ x + (-5) ; 

=  - $\frac{5}{4}$ x − 5 ;  
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→  Now, bring down the "y −1" ;  which goes on the left hand side; 

→  y − 1 = - $\frac{5}{4}$ 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  = - $\frac{5}{4}$ x − 5  +  1  ;
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to get:
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→   "  y = −$\frac{5}{4}$  x − 4 " .
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