Answer:
1.97 units
Step-by-step explanation:
The distance from a point (h,k) to a line [tex]ax+by+c=0[/tex] is given by:
[tex]d=\frac{|ah+bk+c|}{\sqrt{a^2+b^2} }[/tex]
The given line is [tex]6x-y=-3[/tex]. or [tex]6x-y+3=0[/tex].
This implies that: a=6, b=-1 and c=3
The given point is (-2,3)
This implies that: h=-2 and k=3
We substitute into the formula to get:
[tex]d=\frac{|6(-2)+-1(3)+3|}{\sqrt{6^2+(-1)^2} }[/tex]
[tex]d=\frac{|-12-3+3|}{\sqrt{36+1} }[/tex]
[tex]d=\frac{12}{\sqrt{37} }[/tex]
[tex]d=1.97[/tex]
