Solution:
Consider two lines with the following equations:
[tex]y_1=mx+c[/tex]and
[tex]y_2=mx+c_2[/tex]the distance d between these two parallel lines is given by the following equation:
First, we need to take one of the lines and convert it to standard form. For example, take the line:
y = -5x + 26
then, we obtain:
-5x-y+26=0
in this case, we get that
A = -5
B= -1
C = 26
Now we can substitute A, B, and C into our distance equation along with a point, (x1,y1) from the other line. We can pick any point on the line y2. Just plug in a number for x, and solve for y. I will use x = 2, to obtain:
y = -5(2) = -10
then
(x1,y1) = (2,-10)
Replacing these values into the distance equation, we obtain:
[tex]d\text{ = }\frac{|-5(2)+(-1)(-10)+26|}{\sqrt[]{(-5)^2+(-1)^2}}[/tex]that is:
[tex]d\text{ = }\frac{|-10+10+26|}{\sqrt[]{(-5)^2+(-1)^2}}=\frac{26}{\sqrt[]{26}}=5.09\approx5.10[/tex]so that, the correct answer is:
[tex]5.10\text{ units}[/tex]
