Question

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

Answer 1

Answer:

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=\frac{8-4x}{-2}$$y=\frac{8}{-2}-\frac{4x}{-2}$$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!