Answer: [tex]\bold{y=\dfrac{4}{5}x-\dfrac{6}{5}}[/tex]
Step-by-step explanation:
Parallel means it has the same slope. Rewrite the given equation into the form y = mx + b where m is the slope.
[tex]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}}[/tex]
Now use the Point-Slope formula: y - y₁ = m(x - x₁) where
[tex]\bullet \quad m=\dfrac{4}{5}[/tex]
[tex]\bullet \quad (x_1, y_1)=\bigg(\dfrac{1}{4},-1\bigg)[/tex]
[tex]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}}[/tex]
