Question

Find a linear equation whose graph is a straight line with the given property. Through ( 1/4, -1 ) and parallel to the line 4x-5y= 8

Answer 1

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

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.

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

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

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

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

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