Question

What is the equation of a line parallel to 2x - 8y = 3 that contains the point (10, 2)

Answer 1

First, we have to find the slope of the given equation. Let's solve for y.

`\begin{gathered} 2x-8y=3 \\ -8y=3-2x \\ y=(3-2x)/(-8) \\ y=-(3)/(8)+(x)/(4) \end{gathered}`

The coefficient of x is 1/4, which means its slope is 1/4.

Now, we use this slope, the point (10,2), and the point-slope formula to find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-2=(1)/(4)(x-10) \\ y=(1)/(4)x-(10)/(4)+2 \\ y=(1)/(4)x+(-10+8)/(4) \\ y=(1)/(4)x-(2)/(4) \\ y=(1)/(4)x-(1)/(2) \end{gathered}`

Hence, the equation of the parallel line is

`y=(1)/(4)x-(1)/(2)`