Question

e2. Write the equation of the line that passesthrough the point (-2,1) and is parallel to the line4x – 2y = 8.

Answer 1

Explanation:

Let us first convert the equation given into slope-intercept form for better understanding.

subtracting 4x from both sides gives

`4x-2y-4x=8-4x`
`-2y=8-4x`

dividing both sides by -2 gives

`y=(8-4x)/(-2)`
`y=(8)/(-2)-(4x)/(-2)`
`y=2x-4`

which is the equation in the slope-intercept form.

Now we are asked to find an equation that is parrallel to the above equation and passes through (-2, 1).

By parallel, we know that the new equation must have the same slope as the equation above (its slope must be 4).

Furthermore, we need to adjust the y-intercept such that the new equation passes through the point (-2,1).

Therefore, our equation will have the form

`y=2x+b`

Now this equation passes through (-2, 1) meaning it should satisfy x = -2, y = 1.

Putting in x = -2 , y = 1 in the new equation gives

`1=2(-2)+b`

which simplifies to give

`1=-4+b`

adding 4 to both sides gives

`1+4=b`
`b=5`

with the value of b in hand, we can now write our new equation

`y=2x+5`

which is our answer!