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=(4)/(5)x-(6)/(5)}`

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=(-4)/(-5)x+(8)/(-5)\qquad \text{divided everything by -5}\\\\.\quad y = (4)/(5)x-(8)/(5)\qquad \qquad \text{simplifed}\\\\\implies \boxed{m=(4)/(5)}`

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

`\bullet \quad m=(4)/(5)`

`\bullet \quad (x_1, y_1)=\bigg((1)/(4),-1\bigg)`

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