Soluzione - Trovare una linea parallela usando la modalità di intercettazione della pendenza

Plug the coordinates of the point $$\left(x,y\right)$$ and the slope $$\left(m\right)$$ into the line intercept form, $$y=mx+b$$ and solve for $$b$$:

$$x=2$$
$$y=2$$
$$m=\frac{1}{7}$$

$$y=mx+b$$

$$2=\frac{1}{7}·2+b$$

$$2=\frac{2}{7}+b$$

$$2-\frac{2}{7}=b$$

$$\frac{12}{7}=b$$

$$b=\frac{12}{7}$$

plug $$m$$ and $$b$$ into the slope-intercept form, $$y=mx+b$$ :

$$m=\frac{1}{7}$$
$$b=\frac{12}{7}$$
$$y=\frac{1}{7}x+\frac{12}{7}$$

The equation of the parallel line is $$y=\frac{1}{7}x+\frac{12}{7}$$