Question

Find the equation of the line parallel to the graph of – x – 4y = 3 that contains the point (0,1).Write the answer in slope-intercept form.

Answer 1

Let us denote by L1 the line represented by the following equation:

`-x-4y=3`

If we convert this equation to slope-intercept form, we get:

`y=-(1)/(4)x-(3)/(4)`

then, the slope of L1 would be -1/4. Now, the slopes of parallel lines are equal. According to this, we have that the provisional equation of the line parallel to L1 is:

`y\text{ =-}(1)/(4)x+b`

Now, since this line contains the point (0,1), this means that the y-intercept b is equal to 1. So, the equation of the line parallel to L1 is:

`y\text{ =-}(1)/(4)x+1`

then, we can conclude that the correct answer is:

`y\text{ =-}(1)/(4)x+1`