Question

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

Answer 1

The answer is: " y = −
`(5)/(4)` x − 4 " .
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Step-by-step 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 = −
`(5)/(4)`" .
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So:

→ y − y₁ = m(x − x₁) ;

→ y − 1 = −
`(5)/(4)` [x − (-4) ] ;

→ y − 1 = −
`(5)/(4)` (x + 4) ;

→ y − 1 = −
`(5)/(4)` (x + 4) ;

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

We have: −
`(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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−
`(5)/(4)` * x + (−
`(5)/(4)` * 4) ;

= −
`(5)/(4)` * x + (−
`(5)/(4)` *
`(4)/(1)`) ;

Note: Examine the " (−
`(5)/(4)` *
`(4)/(1)`) " ;

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

and we can rewrite the: "(−
`(5)/(4)` *
`(4)/(1)`) " ;

as: " (−
`(5)/(1)` *
`(1)/(1)`) " ;

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

so, rewrite the: "" (−
`(5)/(1)` *
`(1)/(1)`) " ;

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


So:

−
`(5)/(4)` * x + (−
`(5)/(4)` *
`(4)/(1)`) ;

= -
`(5)/(4)` x + (-5) ;

= -
`(5)/(4)` x − 5 ;
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→ Now, bring down the "y −1" ; which goes on the left hand side;

→ y − 1 = -
`(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 = -
`(5)/(4)` x − 5 + 1 ;
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to get:
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→ " y = −
`(5)/(4)` x − 4 " .
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