Answer: " y = [tex] \frac{3}{4} [/tex] x + 4 " .
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Explanation:
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We are given an equation in "slope intercept form" ; that is; in the form of :
"y = mx + b" ; in which "y" in isolated on the left-hand side of the equation; with "no-coefficient" (except for the "implied coefficient" of "1");
in which: "m" is the slope of the line; and the coefficient of "x"; and "b" is the "y-intercept" (or the value of the "y-coordinate" of the graph when "x = 0" ;
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We are given: " y = [tex] \frac{3}{4} [/tex]x − 4 " ;
in which the slope; "m", is "[tex] \frac{3}{4} [/tex]" .
Since we want to write the equation, in slope-intercept form, for the line PARALLEL to the given line; we known that the "line" that is "parallel" will have the same slope".
So we can write: " y = [tex] \frac{3}{4} [/tex] x + b" .
Note that we are instructed to find the "parallel line" that passed through:
"(-4, 1)" ;
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So, in the aformentioned equation, we substitute "-4" for "x" ; and "1" for "y"; to solve for "b" ;
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y = [tex] \frac{3}{4} [/tex] x + b ;
1 = [tex] \frac{3}{4} [/tex] * -4 + b ;
→ 1 = -3 + b ;
↔ b + (-3) = 1 ;
↔ b − 3 = 1 ;
Add "3" to each side of the equation:
b − 3 + 3 = 1 + 3 ;
→ b = 4 .
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Now, since we now that "b" is "positive 4" ; we can write the equation of the parallel line:
" y = [tex] \frac{3}{4} [/tex] x + 4 " .
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