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Liula [17]
3 years ago
5

Find a linear equation whose graph is a straight line with the given property. Through ( 1/4, -1 ) and parallel to the line 4x-5

y= 8
Mathematics
1 answer:
serg [7]3 years ago
6 0

Answer:   \bold{y=\dfrac{4}{5}x-\dfrac{6}{5}}

<u>Step-by-step explanation:</u>

Parallel means it has the same slope.  Rewrite the given equation into the form y = mx + b  where m is the slope.

4x-5y=8\\.\quad -5y=-4x+8\qquad \text{subtracted 4x from both sides}\\\\.\quad y=\dfrac{-4}{-5}x+\dfrac{8}{-5}\qquad \text{divided everything by -5}\\\\.\quad y = \dfrac{4}{5}x-\dfrac{8}{5}\qquad \qquad \text{simplifed}\\\\\implies \boxed{m=\dfrac{4}{5}}

Now use the Point-Slope formula: y - y₁ = m(x - x₁)     where

\bullet \quad m=\dfrac{4}{5}

\bullet \quad (x_1, y_1)=\bigg(\dfrac{1}{4},-1\bigg)

y+1=\dfrac{4}{5}\bigg(x-\dfrac{1}{4}\bigg)\\\\\\y+1=\dfrac{4}{5}x-\dfrac{1}{5}\\\\\\y+1\bold{-\dfrac{5}{5}} =\dfrac{4}{5}x-\dfrac{1}{5}\bold{-\dfrac{5}{5}}\\\\\\\boxed{y\qquad =\dfrac{4}{5}x-\dfrac{6}{5}}

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