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

Solution:

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:

$y=-\frac{1}{4}x-\frac{3}{4}$

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:

$y\text{ =-}\frac{1}{4}x+b$

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:

$y\text{ =-}\frac{1}{4}x+1$

then, we can conclude that the correct answer is:

$y\text{ =-}\frac{1}{4}x+1$