Explicație pas cu pas:
[tex]f: \mathbb{R} \rightarrow \mathbb{R}, \: f(x) = 2x + 3[/tex]
A(1; 0)
[tex]A(x_{A};y_{A}), \: x_{A}=1, \: y_{A}=0[/tex]
[tex]y = 2x + 3 = > 2x - y + 3 = 0[/tex]
[tex]a=2; b = -1; c = 3[/tex]
[tex]d(A,Gf) = \frac{ |ax_{A} + by_{A} + c| }{ \sqrt{{a}^{2} + {b}^{2}}} \\ = \frac{ |2\cdot1 + ( - 1)\cdot0 + 3| }{ \sqrt{{2}^{2} + {( - 1)}^{2}}} = \frac{ |2 + 0 + 3| }{ \sqrt{4 + 1} } = \frac{ |5| }{ \sqrt{5} } \\ = \frac{5}{ \sqrt{5} } = \frac{5 \sqrt{5} }{5} = \sqrt{5}[/tex]
