Respuesta :
The distance between a line with the equation ax + by + c = 0 and a point (A, B) is given by the formula:
[tex]\frac{|aA+bB+c|}{\sqrt[]{a^2+b^2}}[/tex]So, before we can apply this formula, let's rewrite the equation of the line in the form ax + by + c = 0:
y = 2x - 1
2x - 1 = y
2x - 1 - y = y - y
2x - y - 1 = 0
So, in this case, we have:
a = 2
b = -1
c = -1
Also, since we want to find the distance between this line and the point (7, 6), we have:
A = 7
B = 6
Using those in the formula, we find the distance:
[tex]\frac{|aA+bB+c|}{\sqrt[]{a^2+b^2}}=\frac{|2\cdot7-1\cdot6-1|}{\sqrt[]{2^2+(-1)^2^{}}}=\frac{|14-6-1|}{\sqrt[]{4+1}}=\frac{|7|}{\sqrt[]{5}}=\frac{7}{\sqrt[]{5}}[/tex]Therefore, that distance is
[tex]\frac{7}{\sqrt[]{5}}[/tex]